Tag Archives: Connection Games

Connection Games VIII, Part I: ConHex

ConHex is a unique connection game invented by Michail Antonow in 2002.  You may remember that Hex was inspired by Piet Hein’s interest in the four-colour problem, which is related to map-colouring; ConHex makes this inspiration much more explicit.

In ConHex, players compete to claim the corners of spaces on the board until they gain control of half or more on a given space, at which point that space becomes their colour.  The first player to connect their colour’s sides of the board with coloured-in spaces is the winner.  The ConHex board has 41 spaces consisting of a mix of rectangles and hexagons, with 69 playable nodes:

conhex-1

The standard ConHex board, as depicted on Little Golem

ConHex games tend to twist and writhe their way across the whole board, covering much more of the available space than the average connection game.  While there’s a definite lean toward tactics over strategy on the standard-size board, there’s still plenty of intricacy on offer, as we can see in this sample final position:

conhex-sample-game-2

Red wins this game after 52 moves, having connected the two red sides of the board.

How to play ConHex

ConHex offers an interesting twist on the usual pure-placement connection game vibe by adding the additional sub-game of claiming nodes to conquer board spaces.  Rather than simply claiming a space with a stone, a player must vie for control of every space; this adds some intriguing tactics to the game.  In effect, you’re playing the game on two layers: the node-claiming ‘undergame’, and the connection game ‘overgame’ as spaces are gradually claimed.

Here’s how to play:

  1. Two players, Blue and Red in this formulation, vie to be the first to connect the sides of the board marked with their colour with an unbroken chain of spaces under their control.
  2. Blue makes the first move; the swap/pie rule is in effect for the first move of the game.
  3. Players take it in turns to place one counter of their colour on any unclaimed node on the board.  One placed, nodes are never moved and cannot be removed.
  4. If, by placing a node, a player has claimed half of the nodes connected to any adjacent space, then those spaces are then under the control of that player, and a marker piece of their colour is placed with that space.  Once claimed for a given colour a space remains that colour for the rest of the game.
  5. Note that not all spaces on the board have the same number of nodes: edge and corner spaces require 2 out of 3 nodes to be claimed for that space to be claimed by a player; hexagonal and rectangular spaces elsewhere require 3 out of 6 nodes to be claimed; and the central square requires 3 out of 5 nodes to be claimed.
  6. The first player to connect the two sides of the board marked in their colour with claimed spaces wins the game.  Draws are impossible in ConHex.

Here’s some examples of how claiming nodes leads to claiming spaces:

conhex-diagram 1-01

Note that claiming a single node can influence several spaces, and lead to claiming more than one space in a single move:

conhex-diagram 2-01

Tips for beginners

ConHex packs a lot of action into a small space, and the first few plays can feel daunting as you get into pitched battles over every space on the board.  Here are some basic tips to help you get started and get a feel for the game:

  1. Especially in the early game, spread your influence around the board.  Remember that each node influences three neighbouring cells, so try to claim nodes so that you maximise your impact on those cells.  If a neighbouring cell is already claimed by the opponent, think about grabbing a different node that influences still-open cells.
  2. Don’t be a prisoner to your plan!  Once you and your opponent have staked claims around different parts of the board and tactical battles start kicking off, you may find that your initial strategic plan starts to fall apart.  Don’t panic — try to find alternative paths to connect your nodes.  There’s no shame in abandoning your carefully-prepared plan if another path has more promise!  Try to prepare for this possibility early — if you follow (1) above, a nice wide territory can afford you multiple possible paths of connection if one doesn’t end up resolving in your favour.
  3. Use forcing moves to gain tempo.  In turn-based games, when you force your opponent to forget whatever they wanted to do and respond to your move instead, that’s called gaining tempo — gaining time.  In ConHex, the edge and corner cells can be claimed with only two nodes, so these cells can be a good resource for forcing a response from your opponent.  If they see you advancing scarily along the side of the board, they will feel the need to intervene, giving you an opportunity to attack elsewhere and gain the initiative.  You’ll see examples of this in the annotated game below.

Phil Bordelon, creator of the Caeth/Noc/Noeth meta-rules that will be the focus of the second part of this entry in the series, sent me some great strategic tips that should help any budding ConHex (or Caeth/Noc/Noeth) player:

  1. Defend at a distance.  Nodes have a surprisingly large influence on the board in this game, so when your opponent threatens to advance, try to interpose yourself at a distance between them and their connective goal.  Defending directly on cells where your opponent already holds an advantage just lets them gain tempo while not actually containing their advance.
  2. Don’t be afraid to mix it up.  Cells will eventually need resolving as the game goes on, and while you will want to spread your influence wide across the board, you also want to pressure your opponent to commit themselves.  Getting involved in tactical fights will clarify the board situation and push your opponent to reveal their plan, so don’t be afraid to get in there.
  3. Don’t forget the goal.  While resolving cells, remember that the ultimate goal of the game is connection, not just winning control of cells.  If your opponent is threatening cells that you don’t need, let them!  While they’re rejoicing over their new territory, you can be building methodically toward your connective goal.

Note that there’s some tension between these goals — you can’t just claim influence, or fight local battles, you need to balance these elements throughout the game.  Cells can’t be won without tactics, but without a strong connective framework there won’t be anything to fight for in the first place!  These tensions between strategic goals and complex local fights are what make ConHex — and Phil’s meta-games — really interesting.

Annotated Game — Jos Dekker vs mmKALLL

To give you a peek at the strategy and tactics of ConHex, let’s take a look at a game between two high-rated players on Little GolemThis particular game was played between Jos Dekker and mmKALLL, and was quite a back-and-forth contest that lasted 49 moves, which is quite a long haul when you consider the small size of the standard ConHex board.

A quick note on notation: I’ll be using move notation as on Little Golem, where specific nodes are identified by the letter of the appropriate file and the number of the appropriate rank, as indicated below — but I’ve elected not to leave the notation on the subsequent diagrams, because I couldn’t find an aesthetically pleasing board/font combo:

conhex-notation

With that out of the way, let’s pick up the game after four opening moves:

conhex-sample-game-move4

Position after 1. I2 2. H7 3. D7 4. E4

Blue opens in the bottom-right with 1. I2, and in subsequent moves both players stake claims around the centre of the board.  Note that since the edge and corner cells in ConHex require just two nodes to claim rather than three, and the centre cell requires 3 nodes but has lower connectivity than the hexagonal cells, in this game there’s a better balance between central and corner/edge cells than in other connection games.

Note too that while each node may not feel like a big move, each node in fact influences three neighbouring cells.   With that in mind you should try to claim nodes that influence as many cells as possible — claiming nodes on spaces already claimed by the opponent is potentially wasting an opportunity to exert more influence elsewhere.

conhex-sample-game-move8

Position after 5. I7 6. I5 7. J5 8. J4

In the next little sequence, Blue seizes the initiative and jumps in behind Red with 5. I7.  Red would prefer Blue not hold several cells along the edge where Red needs to establish a connection, so this leads to Red responding as Blue marches closer to the lower-right…

conhex-sample-game-move9

Position after 9. J3

…Sadly this leads to Blue claiming two cells at once in the corner, thanks to Blue’s earlier opening move at I2.  This already makes Red’s life a bit more difficult.  Red does have a node advantage on the two rectangles between the centre and the right side, but Blue now has an annoying foothold in the corner.

conhex-sample-game-move18

Position after 10. I10 11. E9 12. G8 13. C5 14. C2 15. D3 16. F2 17. B3 18. A1

Red responds with due caution by claiming a node at the top-right corner, to make absolutely sure Blue cannot block off the whole right side.  Blue responds by starting a framework of nodes cascading down the left side, while Red bolsters their strength in the centre, eventually running all the way down to the bottom-left corner and claiming it.

The stage appears to be set for the coming battle: Blue appears poised to attempt to cut across the board diagonally across the centre, while Red perhaps will look to connect the top-right and bottom-left corners.

conhex-sample-game-move22

Position after 19. E2 20. D2 21. F3 22. G2

Blue now immediately starts a battle along the bottom edge, building on the earlier node at D3, claiming a new cell and pushing Red to commit to more nodes along the edge.  Red appears stronger down here, but Blue remains in a position to claim the two other spaces incident to D3.

conhex-sample-game-move24

Position after 23. I8 24. H9

Before pursuing that advantage, however, Blue jumps north toward Red’s upper-right corner, forcing them to respond at H9 to avoid further Blue cells getting in the way of Red’s plan to connect across the centre.

conhex-sample-game-move27

Position after 25. G3 26. D5 27. C4

Now Blue jumps back south, evening up the score 2-2 on a second rectangle along the bottom edge.  Red responds in kind with 26. D5, forcing Blue finally to claim the two lower-left cells with 27. C4.

conhex-sample-game-move29

Position after 28. C7 29. C6

Red again jumps into a Blue-majority cell with 28. C7, and again Blue responds by taking two cells in one with 29. C6.  After these tactical scuffles, Blue appears more robust for the time being, with seven cells claimed compared to Red’s four.  But Red may still try to move north from the southern edge, and retains control of the upper-right corner.

conhex-sample-game-move32

Position after 30. H3 31. H5 32. G4

Indeed Red does push northward, curling around Blue’s outpost of five squares in the lower-left quadrant of the board.  Red is threatening to connect to the upper-right corner — a play at H6 or I6 would do the trick, but Blue can defend.

conhex-sample-game-move36

Position after 33. H6 34. E8 35. F8 36. D9

Blue of course spots this threat and responds at H6 without hesitation, preventing the north-south connection for Red.  Red then moves to shore up their defences, claiming a cell just above Blue’s lower-left cluster to make their job a bit tougher, and threatening to connect horizontally to the upper-right corner.

conhex-sample-game-move39

Position after 37. F9 38. F7 39. E6

Blue responds by blocking the possible Red claim with 37. F9, and Red begins to move toward the centre.  Blue’s response at E6 leaves Red’s upper-left cell somewhat isolated.  Clearly at some point a battle will rage over these last few central cells….

conhex-sample-game-move43

Position after 40. E10 41. G10 42. J7 43. J6

For now, though, Red jumps north to attempt to bring their upper-left cell back into the game, and to constrain Blue’s options.  If Blue wants to connect their rightward cells to the central and leftward ones, they will need to either snake through the centre or sneak around Red’s upper-right corner, but Red still holds an advantage there.  Red follows this up with 42. J7, which forces Blue to respond at J6; Blue may now hold two more cells around J6, but Red remains strong in the corner and is now ahead one node in cell incident to J7.  Blue’s only path to connection is now through the centre of the board.

conhex-sample-game-move45

Position after 44. F4 45. G6

Red now makes a move on the centre first, claiming two central cells with 44. F4 and building on their chain of cells leading from the lower-left corner.  Blue moves in as well with 45. G6, and now the central cell finally comes into play.

conhex-sample-game-move47

Position after 46. F6 and 47. F5

Blue however is a tempo ahead in the centre, so Red’s attempt to claim is immediately short-circuited by 47. F5.  Blue is now connected from the bottom-right corner all the way through the centre, and is only two cells away from a winning connection to the northern edge.

conhex-sample-game-move49

Position after 48. F10 49. H10 (1-0)

Red makes a last-ditch effort to get in the way with a play at F10, but Blue simply claims two cells at once with H10 and wins immediately.

So there we have it — a good example, I think, of what an exciting game of ConHex looks like.  By the end the players had fought for dominance in nearly every part of the board, and each individual node caused a cascade of tactical complications.

 

Super-Sized ConHex

As you can see, ConHex manages to pack quite a lot of excitement into a small board, but as you probably have noticed by now I’m a fan of playing on larger boards in general.  As it turns out, several people expressed a desire for larger ConHex boards on BoardGameGeek too, so I jumped at the chance to construct these monsters (also available in PDF):

Click on the images to retrieve 300-dpi images of these boards, if you prefer that to the PDFs at the BGG link.  To give you a sense of scale — if you print ConHex+5 so that each node is 22mm in diameter (same size as a standard Go stone), you’ll need a mat about 77cm on a side (a bit over 30 inches).  Soon I’ll be adding black and white versions of the boards to the filepage as well, in case you do prefer to use Go stones.

Each of the plusses represents an additional outer ring of perimeter cells.  I’ve maintained the basic geometry of the regular board, so the edge and corner cells are still quicker to claim, but offer less connective options than central cells.

If you do try using any of these, please let me know whether you enjoyed the experience!  I’d like to find out which board sizes lead to greater strategic sophistication without making the play experience too overwhelmingly complicated.

Playing ConHex online

ConHex is fairly well-known, as far as connection games go, so there are several good options for online play.  Compared to some of the more obscure connection games you should be more than able to find some opponents.

For correspondence play, Little Golem of course is popular — in fact all my diagrams and expanded boards here are based on their version of the ConHex board, which I find the most visually appealing and practical.  Richard’s PBEM Server is another popular place to play, and ConHex can be played using the server’s graphical web interface.

For real-time play, I’d recommend igGameCenter.  This site is usually pretty active, and if you jump into the chat on the main page you can normally find someone willing to play their large selection of connection games.  Yucata.de is another option — I haven’t personally used this site before, but the ConHex page shows a number of players who’ve played hundreds of games of ConHex, so presumably finding an opponent wouldn’t be too difficult!

I should note that as far as I can tell, every site uses the standard board only — I seem to be the only oddball who created some larger ones.  However if anyone out there wants to try playing on the larger board(s), do give me a shout!

Buying ConHex

If you prefer physical games over virtual, luckily ConHex is one of the relatively small number of connection games popular enough to actually have been published in official form.  The game was published for the first time in 2005 and has been continuously available ever since, including in this gorgeous wooden edition by Gerhards Spiel und Design:

conhex-kugeln-aus-halbedelstein-light

Nestor Games in Spain also offers this portable edition on a sturdy neoprene mat with plastic pieces:

nestor-conhex-reg

Nestor also offers a deluxe edition, with a larger laser-cut acrylic board:

nestor-conhex-deluxe

It’s true that ConHex can be played using print-and-play boards with pieces for other games you may have lying around, but there’s something to be said for owning a purpose-built set.  ConHex is fortunate enough to have several high-quality editions available simultaneously, so do take a look at these if you’d like to give the game a try offline.

The origins of ConHex

According to Cameron Browne in Connection Games: Variations on a Theme, ConHex is derived from Michail Antonow’s earlier game called Pula.  Pula is played on a hexhex-4 board — I’ve mocked up a quick example below — where players claim vertices of the hexagons in order to claim spaces, as in ConHex.  Rather than aiming for connection across the board, however, players simply vie to control the most hexagons on the board.

Pula

Apparently Antonow also developed a follow-up game called Pula 2, where players instead aim to gain the most points according to this scoring system:

  • 1 point for connecting adjacent sides of the board with a chain of hexagons in their colour
  • 3 points for connecting non-adjacent sides
  • 5 points for connecting opposite sides

Pula 2 sounds like it might be quite interesting — I’m generally a fan of point-scoring connection games, and the multiple possible connection types could lead to some complex tactical considerations.  However I expect it would shine more on a somewhat larger board than hexhex-4.

More importantly, what Pula shows us is that the vertex-claiming mechanic of ConHex is actually pretty flexible — it can function very well in other games too.  Lucky for us, Phil Bordelon independently discovered this fact in 2004 and invented the Caeth and Noc meta-rules — rules that can be used to modify nearly any connection game.  In Noc games, players claim spaces by claiming vertices as in ConHex, whereas in Caeth games players claim edges of spaces.  Fifteen years later he also gave us Noeth, where players have to claim a half of the vertices and the edges of a space in order to claim it — and the 12* move protocol is used as well.  With these meta-rules, any connection game can gain an additional ‘undergame’ like we see in ConHex — and Phil’s rules significantly extend the undergame concept.

In part II of this post, and in collaboration with Phil, I’ll focus on these meta-rules and discuss how they can inject some new life into our favourite connection games.

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Connection Games VII: Onyx

Today I’m going to talk about a game with a highly unique visual presentation and capture mechanism: Onyx.  I’m really fascinated by this game, which is helpful, because making all the boards and diagrams for this post took a lot of time!

Onyx was published by Larry Back in the year 2000 in Abstract Games Magazine Issue 4.  The board geometry immediately stands out — the game takes place on the intersections of an Archimedean tiling of squares and triangles (well, technically all triangles but the squares are important in this game):

onyx-12x12-plain-dots

Besides being immediately visually interesting, this board tiling creates interesting variations in connectivity for different points on the board.  The intersections at the centres of the squares are relatively weaker points, as they only connect to four adjacent points — but as we shall see, playing at these weaker points is sometimes essential.

How to play Onyx

Onyx is part of the relatively small portion of the connection games family that includes a capture mechanic, whereby enemy pieces can be removed from the board.  The capture rules are unique and need some explanation via diagrams, so first I’ll cover the basic rules and then explain capture in detail.

The basics:

  1. Two players, Black and White, compete to form connections across the surface of the Onyx board.  Black must form an unbroken chain of pieces connecting the top and bottom edges of the board; White must form an unbroken line of pieces connecting the left and right edges of the board.  Intersections at the corners of the board are considered part of both sides to which they are connected.  Draws are not possible in Onyx
  2. Before the game starts, the players can choose whether to play the standard variation, where four White pieces and four Black pieces are placed on the marked points of the appropriate colour at the start of the game.  In the open variation, the game board starts empty.  (Note: both variations are very playable; the standard variation has the advantage of increasing the importance of the sides and corners of the board during the game).
  3. Black moves first, placing a single stone on any empty intersection of the board.  The swap rule is in effect for the first move of the game, so the second player may either swap and take Black, after which the first player is now White and plays a White stone in response, or the second player may stay as White and play a White stone.
  4. Each turn, a player may place one stone of their chosen colour on any empty intersection of the board.  However, a piece may not be placed on the intersection in the centre of a square if any pieces are already placed on the corners of that square.
  5. Once placed, stones may not be moved.  Pieces can be removed from the board via capture (explained below).  Captured pieces are removed and returned to the player of that colour.  Points on the board vacated by captured pieces are free to be played on subsequently by either player.

Here’s a completed game of Onyx won by Black.  The pieces highlighted in red show the winning vertical connection:

onyx-12x12-sample-game-1 -completed

Capturing Rules

Capturing in Onyx is about forming a particular pattern.  Basically, if on your turn you are able to complete a pattern in which a square area on the board has two of your pieces at diagonally adjacent corners, and two of your opponent’s pieces on the other diagonally adjacent corners, and the centre point of the square is unoccupied, then your opponent’s pieces on that square are captured:

onyx-capture-diagram-01

Here White places a piece on the corner of the square, which completes the capturing pattern. The two Black pieces are captured and removed from the board.

Double-capture is also possible, if a single move leads to the completion of this capturing pattern on two squares at once:

onyx-double-capture-diagram-01

In a double-capture White places a piece at the intersection of two squares, and manages to complete the capturing pattern on both squares simultaneously.  All four Black pieces are then removed from the board!

The capturing mechanic in Onyx leads to some interesting consequences.  Recall that you may only place a piece at the centre point of a square when no pieces have yet been placed on the corners.  This means that capture can be prevented, but requires you to place a piece on a weaker point.  The possibility of capture also prevents a player from easily blocking the other on the diagonals, and prevents deadlocks in general from grinding the game to a halt.

You might notice that after a capture, the captured player can immediately threaten a re-capture by placing a piece on one of the newly-emptied corner points.  As a result you’ll often see a sequence like this:

onyx-capture-diagram-sequence-01

White starts the sequence by capturing.  Black responds by making a re-capture threat on one of the vacant points.  Finally, White ends the threat by placing a stone on the remaining empty point — now no more captures can happen on this square.

Making connections in Onyx

Given the unique board geometry and the capturing mechanism in this game, there are some novel types of connections that you don’t see in other connection games.  I will summarise some key connection types and show some examples of sequences of play that can result.

Onyx has a basic connection between pieces that is the equivalent of the bridge in Hex — the diamond, a simple but strong connection where any attempt by the opponent to break it can be answered easily:

onyx-diamond-01

Here White establishes a diamond connection.  Black’s attempt to break it is easily answered on the other empty point of the diamond.

Less secure than the diamond is the square — an attempt to break this connection can result in a secure connection as seen below, but a clever opponent might find a way to divert your attention elsewhere and capture your two pieces instead.

onyx-square-01

White establishes a square connection.  Black attempts to cut across the diagonal, but White answers by filling the last remaining corner.

Next up is the housewhich is very secure.  There is no threat of a capture here, so only a deadly double-threat forcing a response elsewhere on the board can allow this connection to be broken.

onyx-house-01

White builds a house.  Black’s anaemic attempt to break it is easily countered by playing on the remaining empty point.

Unusually, Onyx has a connection that benefits from the presence of an opposing stone.  Larry Back calls this a duplexbecause it resembles a house containing two different families.  In isolation this connection can be secure, but the presence of the opposing piece makes it a bit easier for the opponent to generate threats that require a response outside the duplex formation.  If the threat of a cut is stopped by a capture, the opponent can also threaten recapture, which gives another opportunity to generate threats elsewhere.

onyx-duplex-01

White builds a duplex.  Black attempts to cut, but that simply leads to a capture by White and a complete connection (for the moment).

Most importantly we have the long diamond connection.  This connection initially looks precarious — there’s a long distance between the connected pieces.  However, the long diamond is actually quite strong:

onyx-long-diamond-safe-01

White forms a long diamond connection.  Black attempts to block a connection, but that leads to a capture by White.

However, here we see an instance where playing on the weak point at the centre of the square pays off.  Black can break the long diamond connection, but at the cost of three moves, one of which is on the weak centre point:

onyx-long-diamond-broken-01

Black successfully breaks the long diamond connection with a play to the centre of the square.  White has no way through.

The long diamond can also be used defensively.  If a player plays their stone at the end of what could be their opponent’s long diamond connection, this is called an opposition long diamond.  Here’s an example of how the opposition long diamond can be effective, assuming White attempts to bludgeon their way through directly rather than playing around the obstruction:

onyx-opposition-long-diamond-01

Black plays an opposition long diamond formation.  White attempts to push through, but Black can simply capture.

This is a very simplistic continuation — for more sophisticated discussion of the opposition long diamond, please see Larry Back’s article in Abstract Games Issue 11.

The long diamond connection is a very important part of Onyx.  Understanding this connection allows you both to play these connections effectively and to block them.  Given that the long diamond allows connections to grow more quickly across the board, it’s very important to know how to deal with them.

 

Tips for playing Onyx

Bearing in mind I’m very much a beginner in this game, from my reading and my early experiences getting absolutely ruined by Larry Back on the Gorrion Server I can offer a few tips that might help you get started.

  1. Know your connections!  Get familiar with the basic types of connections outlined above.  Play around with different attempts to make or break connections in these formations.  The more comfortable you are with these basic connections, the more quickly you’ll be able to recognise effective moves in a given board position.
  2. Don’t ignore the sides and the corners.  Particularly in the standard variation, where pieces are placed in the centres of the board edges at the start of the game, pay attention to the sides and corners of the board.  Playing in the centre is valuable too, but if you don’t take care of the sides and corners, your opponent can get a lethal head-start on a strong connection along the side of the board.  In the early game, balance your plays in the centre with plays in the corners (but not too deep in the corners).
  3. Don’t forget — your own stones can be a liability! Unlike in games like Hex or Y, where having extra stones around is never bad for you, in Onyx carelessly-placed stones can help your opponent.  As we saw above, the strong duplex connection can be formed using an opponent’s stone!  A badly-placed stone might also hurt your later attempts to connect stones by opening you up to a capture.  Try to avoid placements that open up tactical advantages for your opponent!  Conversely, if you can force your opponent to play a move that weakens their position — say, by giving you an opportunity to build a duplex — then go for it.
  4. Watch the diagonals!  Like in other connection games, in Onyx you can end up in ladder formations, where both players are matching each other move-for-move as they make their way across the board.  In Onyx these ladders have been dubbed snakes by designer Larry Back, and look like this:
onyx-ladder-01

A typical snake formation.  Both players are writhing their way across the board, playing solely along opposing edges of the squares to avoid the possibility of a capture.

Because of the possibility of a snake forming, and the dire consequences if your opponent gains an advantage in these situations, it’s important to pay attention to the development of play along crucial diagonals on the board.  Don’t just let your opponent set up shop along the diagonals!

Again these are very basic tips, but if you keep these ideas in mind while playing you can at least find some semi-sensible moves to play and get a feel for how the game works.  After working with these basic ideas for awhile, do check out Larry Back’s articles in Abstract Games — particularly the tactical tips in Issue 6 and the deeply-annotated sample 12×12 game in Issue 11.  Those articles go into much more detail on the concepts I’ve mentioned here.

From there, Larry’s article in Abstract Games 17 about edge templates will be valuable for the advanced player.  Edge play is complex in this game, and knowledge of these template positions will give you critical insight in these moments, where sometimes only one move will allow you to connect or to block your opponent.

 

Sample 16×16 game

Since Larry Back already annotated a 12×12 Onyx game in Abstract Games magazine issue 11 at a much deeper level than I could, I thought I’d do a quick walkthrough here of a 16×16 game.  Right from the start let me say that this is just my reading of the game — I’m sure I’m missing things here.  But, as with learning Go, reviewing games and trying to understand why moves were played is a great way to improve, so hopefully any future game reviews I do will get better over time!

Like other connection games, Onyx is highly scalable, and larger boards can be used to provide a greater strategic challenge.  The 16×16 game seems to have a nice balance between depth and game length — games are complex and interesting, but don’t wear out their welcome.  You can play 16×16 and 20×20 Onyx online at the Gorrion Game Server, or you can print out my PDF boards (16×16 and 20×20) and play face-to-face.

The game below was played on the Gorrion Server between the server’s founder, dashstofsk (playing Black) and larry_back (the game’s inventor, playing White).  Let’s pick things up 8 moves in:

 

onyx-16x16-sample game 1-move8

Position after 1. C6 (swap) 2. E12 3. K11 4. L5 5. H8 6. F4 7. H4 8. H9

This game is using the standard variation, in which Black and White start with four pieces each on the sides of the board.  Initially Larry opened with C6 in the lower-left corner, but dashstofsk elected to swap, so from this point on Larry played White.

In the opening phase here you can see both players staking out territory.  Black has laid claim to the lower-left and upper-right corners, while White is camping out in the upper-left and lower-right.  Note that all four of White’s pieces are sitting precisely on the board’s main diagonals!

onyx-16x16-sample game 1-move18

Position after 9. K8 10. J7 11. I8 12. I9 13. N10 14. J9 15. J8 16. L12 17. F12 18. K12

 

Ten moves later, both sides have built up a bit of a wall in the centre of the board — some structure is starting to develop now after the opening.  Black has cut off any of White’s ambitions to connect J7 and J9, and at the end of this sequence White has blocked Black from venturing north from K11.  Still plenty to play for at this stage.

 

onyx-16x16-sample game 1-move26

Position after 19. G12 20. G10 21. M12 22. L11 23. N11 24. M8 25. K9 26. LM910

After 26 moves, both sides are starting to probe their opponent’s defences.  Black’s initial extension at G12 is promptly stifled by White forming a diamond at G10.  White follows up by venturing south from L11, further complicating Black’s hopes of heading north.  At the end of this sequence both sides have overlapping long diamonds over the square spanning the L and M files and the 9th and 10th ranks; White spends a move playing on the centre of that square, aiming to block Black from connecting their long diamond and securing a connection vertically for themselves.  From here Black needs to consider starting a new adventure elsewhere on the board.

A note about move notation — the central intersections in the squares on the board are actually located between the rank and file designations around the edges of the board.  However, we can identify a central point by the ranks and files covered by the square in question — so in this case, we can notate White’s move 26 as LM910.  For future reference, moves that lead to a capture are followed by an asterisk, and a double capture by two asterisks.

onyx-16x16-sample game 1-move38

Position after 27. I11 28. J12 29. J11 30. I12 31. H11 32. E15 33. FG1516 34. F15 35. G15 36. G14 37. I14  38.  G13

Following the last exchange, Black gamely heads west, eventually building a diamond connection to G12 with 31. H11.  Seeing no more profit to be made here, White suddenly jumps north, forming a long diamond with 32. E15 — but Black quickly responds by playing at the centre, blocking off the long diamond.  White, undeterred, veers south and links G13 to I12 with a duplex connection.  White now has a dangerous-looking chain stretching all the way from E15 to M8.

onyx-16x16-sample game 1-move46

Position after 39. O5 40. O4 41. N5 42. N4 43. L7 44. M4 45. M6 46. OP67

Seeing the danger, Black attempts to regain the initiative with 39. O5, starting a new front against the right edge of the board.  White quickly jumps in to block any attempts to connect further south, and after a few more exchanges White has a strong wall keeping Black hemmed in.  This culminates in White spending a move disrupting Black’s long diamond between O5 and P8.

So far Black’s attempts to make progress along this edge are not bearing much fruit.

onyx-16x16-sample game 1-move54

Position after 47. N7 48. F5 49. G4 50. E1 51. G2 52. G5 53. I5 54. I4

Black plays a final move along the right edge here, building a house with 47. N7, which also prevents White from forming a diamond at the same point and potentially making something useful out of the stone at OP67.  Sensing again that a change in focus is needed, White jumps over to the lower-left corner with 48. F5.

After a few more moves, Black has formed a second house connecting G2, F4 and G4, which also prevents a diamond from White between H1 and G2.  White remains resourceful, however, and jumps sideways with 54. I4, forming a duplex with the stones at G5 and G4 and reaching over toward his line of stones starting at L5.  We can see now that White’s opening moves are paying off here — by having some stones placed early in key corners along critical diagonals, he’s ensured he would have some options at this later stage in the game.  If Black had full control of this corner, White would not have much counterplay here and would need to start fresh elsewhere.

onyx-16x16-sample game 1-move60

Position after 55. L4 56. K5 57. K4 58. K7 59. L8 60. I6

Things are starting to get a bit desperate for Black.  White extends the line of stones on the lower-right with 56. L4, then jumps north with 58. K7, with a threat to punch through Black’s line of stones and connect to M8.  Black responds swiftly, closing that door with 59. L8.

But White’s response at 60. I6 looks strong — with that one move, he forms another duplex connection between G5, I5 and I6, and threatens to connect to the line of stones at K5.  Black’s interposing stone at I5 is an annoyance, but now White appears to have two possible paths around it.

onyx-16x16-sample game 1-move68

Position after 61. D5 62. E5 63. C7 64. E4 65. A3 66. C4 67. AB45 68. B6

Black sees White is attempting to complete his chain across the 4th and 5th ranks, and mounts a defence with 61. D5, forming a diamond connection with C6.  White responds by strengthening his chain with 62. E5.  Black seems to anticipate a move northwards and blocks at C7, but that leaves White the opportunity to connect at E4.  Black attempts to wall off the edge with 65. A3 and 65. AB45, but White’s responses at C4 and B6 seal with deal.  White now has an unstoppable connection to the left edge from B6, a duplex connection from there to C4, an unstoppable connection to the right edge from O4, and two ways around the interposing stone at I5.  Black sees the writing on the wall and resigns.

If they’d played to the end, we might have seen a final position something like this:

onyx-16x16-sample game 1-extended

Position after a possible continuation 69. A6 70. A5 71. B5 72. C5* 73. B5 74. C6 75. J5 76. K6 77. P5 78. P4 79. H6 80. H5, White wins

I’m not going to pretend my hypothetical continuation here is by any means best play in this situation, but I think we can be reasonably confident that there was not too much Black could do here.  White has enough options for connection at each key point in the chain to fend off Black’s defensive tries.  Ultimately I think White’s strong opening, securing key points along the main diagonals, and later the deft manoeuvring near the lower-left edge and around the Black stone at I5 secured the win.  With that clear path through the centre and all the way to the left edge, White ends up with a completed connection between A5 and P4.

Hopefully this sample game gives you some idea how an Onyx game feels in play.  On the 16×16 board I think the game really shines; more strategic options open up, play often bounces around disparate parts of the board, and yet each move still feels consequential.  My currently ongoing 20×20 game with Larry is, to my knowledge, the first one ever played, so I’ll reserve judgment on that board size until we at least finish one game!  If pressed, I’d probably say it seems interesting thus far, but definitely too large for a beginning player like me to have much of a chance against Larry.  Nevertheless I’m enjoying myself.

 

Next steps

As mentioned above, if you want to play Onyx I recommend the Gorrion Server, which offers 12×12, 16×16 and 20×20 boards, all with either the standard variation or the open variation.  The web interface also allows you to play out moves for both sides on the board to check variations, which is very convenient.  The server needs more players, so please join us!

Alternatively, you can play Onyx on Richard’s PBEM Server — however, here you can only play 12×12 (standard or open variation).

To learn more about the game, your best port of call is definitely Larry Back’s articles in Abstract Games magazine.  He offers basic tactical advice, annotated games, and puzzles to sharpen your tactical vision.  Other than that we don’t have much more strategic advice out there — so please come play with us online, and help us discover more about what this fascinating game has to offer!

I’m not 100% sure what I’ll feature next in this series — at the moment I’m leaning toward covering ConHex and Phil Bordelon’s related meta-rules.  At some point as well I’ll cover Gonnect, then circle back to cover Christian Freeling’s two predecessors to Starweb, YvY and Superstar.  He apparently doesn’t like either of those games very much anymore, but I’m interested in the various descendants of Star so I’d like to write up something on these games.

Thanks for reading — if you know of a connection game that might fit my tastes that I haven’t mentioned, do get in touch and I’ll investigate it and write about it further down the line.  Part of my motivation for doing all of this is to open my mind up to new games, so I’m very happy to take suggestions!

 

 

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Connection Games Part VI: Twixt

As promised, today we’re going to take a look at TwixT — a classic connection game designed by Alex Randolph in 1962.  Twixt (I’m giving up on the second capitalised ‘T’ because I’m just going to keep forgetting it anyway) is one of the relatively rare connection games that actually was released in physical form — and copies are still readily available via Ebay and used board game sites.  I have a copy of the 1962 3M bookshelf edition, which looks like this:

twixt-pic2

twixt-pic4

The game is played on a 24×24 square pegboard, and each player is armed with 50 pegs of their colour — Red or Black — and 50 bridges that span between those pegs, as in the photo above.  Each player strives to complete a continuous path of linked pegs reaching connecting their sides of the board.

So far, so similar, right?  But what sets Twixt apart is that, despite the seemingly enormous size of the board, games resolve quickly — and fiercely.  Twixt is a highly tactical game — David Bush estimates that the game is about 80% tactics on the standard-size board — and the tactics are razor-sharp.  By that I mean a single mistake can be very costly in this game, and sometimes what constitutes a mistake isn’t immediately obvious.

The upshot of this is that Twixt rewards careful play, deep calculation of possible continuations of each move, and substantive study of tactical principles.  It’s a tense and exciting game, and in my opinion one well worth learning.  I can’t possibly cover all of the myriad complexities of Twixt in one post, of course, and I’m only a beginner myself, but luckily 3-time Mind Sports Olympiad Champion David Bush has helped me tremendously by providing general tactical tips — with examples! — and a fully-annotated game on a small board.

We’ll start with the rules and an overview first, then we’ll move on to tactics, and finally the annotated game.

The Rules of Twixt

Like the other connection games we’ve covered, Twixt is quite easy to learn.  This is how it works:

  1. The Red player plays first.  After Red makes their first move, Black may invoke the swap/pie rule on that move only — if Black chooses to swap, they are now Red, and Red now becomes Black and makes Black’s first move.  Alternatively, players may swap and keep their initial colours by reflecting the opening move across the main diagonal and replacing the peg with a Black one, then playing on from there.
  2. Each turn, players may do the following:
    1. Remove as many of your own links from the board as you like — usually not necessary, but sometimes helpful to clear up the play area somewhat.
    2. Place one peg of your own colour in any vacant hole on the board, except your opponent’s border rows (the single rows behind the lines of your opponent’s colour, as seen in the picture above).
    3. Place as many legal links of your own colour as you like.  A legal link is available when two pegs are one ‘knight’s move’ apart — in other words, they are at opposite corners of a 2×3 six-peg rectangle.  No links may cross each other.
  3. The first player to connect the sides of the board marked in their colour with an unbroken chain of links wins the game.  If neither player is able to do this, the game is a draw.  Draws are very uncommon in Twixt, generally speaking.
  4. Players of different skill levels may elect to play a handicap game, in which the stronger player concedes a starting advantage to the weaker one.  The smallest handicap, for use between two players rather close together in strength, would be to allow the weaker player to take the first move while denying the stronger player the option to invoke the swap/pie rule.  From there, players may elect to use row handicapping — here the weaker player’s two sides are moved closer together by removing some rows from the board, making their task easier.  In these games the weaker player is always Red and always plays first.

Note that the annotated game from David is a row-handicapping game, which will nicely show off this excellent feature of Twixt.  Relatively few connection games have straightforward options for handicapping between players of disparate ability; Twixt’s row handicapping makes these kinds of matches just as tense and exciting as any other!  Row-handicapping is supported in real-time Twixt play on igGameCenter, too.

Another nice property of Twixt that it shares with most connection games is its scalability.  The default board is of course the 24×24 pegboard shown above, but the game plays well on both smaller and larger boards (within reason).  Little Golem has recently added options for play on 30×30 and 48×48 boards, and as with other games like Hex, larger board sizes add extra strategic wrinkles to a game of Twixt.  For a very detailed preview of 30×30 Twixt, do take a look at this deeply annotated game by David Bush on BoardGameGeek.  David says this about 30×30:

In a standard game, a player might make four or five moves, usually in the opening, which are based mainly on intuition. The rest of the game is spent attempting to tactically justify the plan you are now stuck with. A larger grid allows a much greater variety in the shape of your strategical plan, and offers a better balance between intuition and calculation.

Having said that, for the beginning player, it may be worth starting first at a smaller size — say 18×18, or a handicap game with a stronger player — before graduating to standard 24×24, then think about trying games on larger grids once you become well-acquainted with the standard board.

As has become my custom in this series lately, I’m going to show you a few final positions of some Twixt games below so you can get an idea how a game might look.  First, let’s take a look at a 24×24 game from Richard’s PBEM Server:

twixt-sample-24-1708

In this game Red resigned after 41 moves, and we can clearly see why — Black has a continuous, unbroken connection across nearly the entirety of the board, and will easily finish a complete connection within a few moves.  Red made a fairly scattershot attempt to block Black’s progress, but ultimately Black was undeterred and deftly slithered straight across the middle of the board.

Here’s another 24×24 game, this time a more intense tactical battle:

twixt-sample-24-1487

This time Red resigned after 57 moves — this is quite long for a Twixt game!  Clearly both sides made several abortive attempts to get a strong connection going, and the battle raged across most of the board.  Ultimately Black was able to find some order amongst the chaos, building up the circuitous connection we see at the bottom of the board.  Red sensibly threw in the towel at this point, as by this point Black has a stronger connection as well as numerous ways to stymie any attempts by Red to get something going.

Let’s take a quick look at one more 24×24 game — this one was played on Little Golem between David Bush and a strong AI called TwixtBot.  This game was played at a very high level, far beyond my ability to talk about sensibly, but you can take a look at some detailed analysis of this game on its entry at the Twixt Commentator website.

twixt-sample24-twixtbotvDB

Twixtbot is playing White — Little Golem uses White and Black instead of Red and Black –while David is playing Black.  Black resigned here on the 50th move of the game (White’s last move is highlighted in red).  Again I’m not able to analyse this game in detail, but you can see that despite Black’s hold on the centre of the board, White has been able to cut off Black on the left and prepare the ground for a connection along that edge of the board.  I recommend taking a look at the game via the link to Twixt Commentator above — when you step through the moves one by one, and click through the variations in the comments as well, you can get a taste of how intricate Twixt tactics can be at high levels of play.

Finally, since I’ve already linked you through to David’s deep commentary on a 30×30 game, I’ll briefly show off a sample game at 48×48.    Now, 48×48 games are long, and not commonly played, and this particular game has nearly an 800-point rating difference between the two players, but nevertheless you can get an impression of how challenging games at this size will be:

twixt-sample48-2

White was the player with the sizeable rating advantage, and in the end Black resigned after 72 moves.  White clearly had the upper hand here from the beginning, and lived up to their rating by methodically winding their way through Black’s defences.  48×48 has yet to achieve the growing following we see for 30×30, but I hope at some point it does take off a bit more — I’d be fascinated to see what pitched battles between strong players would look like on this enormous playing area.

Twixt Tips for Beginning Players

Now I’m going to turn things over to David Bush, who has kindly offered up some useful core principles for new Twixt players:

  • The ONLY way to win is to block your opponent on the whole board. More so than with most other pure connection games, there is a difference between making a nice pattern for yourself and blocking your opponent. The latter should always take priority.
  • Play lightly.  Just because you put some pieces on the board does not mean you have to use them in your final winning path. Be ready to start a new path if the opportunity arises.
  • Focus on tactics.  Try our hand at these interactive puzzles which can occur in a real game.  In my opinion Twixt is at least 80% tactics.
  • NEVER play Twixt before breakfast.

Let’s take a bit of a deeper look at some of these points.  Note that these examples below are quite sophisticated, and perhaps challenging for a new player.  I recommend following along with some helpful Twixt software like JTwixt (needs Java to run), which will allow you to place moves on the board and try possible alternate variations, or T1j (also needs Java), which is less full-featured when it comes to analysing games but includes a computer opponent to try your moves against.

The Only Way to Win is to Block

Here is a typical opening position:

must_block1

Black has just played i14. In the game, Blue answered with K11.

must_block2

This 3-3 relationship with H8 is called a tilt setup — Blue can make a single move that connects these pegs in two different ways. This is all well and good, but it’s too slow for Twixt. Black played N16.

must_block3

This 5-2 relationship with i14 would take two moves to complete a connection, but such a connection can form in a variety of ways. You can see the network of possible linking paths is like a diagram of a cube. This is a very resilient pattern. It is difficult for Blue to find a way to attack through that gap. Blue tries to block on the right with P16.

must_block4

You can see that P16 is on a line that leads to W2. Black could start a race toward the upper-right corner with P15 — a ladder chase — but Blue could simply follow that line to W2 and win the chase.  But Black N12 is much stronger.

must_block5

Black has a commanding advantage here. Instead of K11, blue might have played O13.

must_block6

This is not as well connected to H8 as K11 was, but that’s not as important as stopping black from achieving an easy win through the middle of the board. Blue has threats now to connect O13 to the top and to the bottom. This is a much more balanced position.

Play Lightly

This position is from a game between two versions of a Twixt bot. The bots are crushing heads these days. At least one human is probably still stronger as of Spring 2020.

play_lightly0

Black abandons its pegs at F4 and L5 to start a new battle along the bottom. A couple moves later we get this:

play_lightly1

To a player with some experience, S21 looks doomed. But that’s the point. S21 is a feint, a threat that blue has to respond to. As blue keeps adding pegs to the bottom right, black will improve its connection to the left, and then switch to an attack elsewhere along the right edge. Here is the game several moves later:

play_lightly2

Blue’s group in the bottom right is almost useless. Black gave up pegs at F4, L5, and S21 for the sake of gaining an overall advantage across the board.

Here’s a more typical example. Note that the blue borders are on the left and right here.

play_lightly3

This 4-1 blocking pattern between i6 and E7 is often the best way to conduct a corner battle. Black is willing to abandon the i8 group in some variations, in order to gain an attack down the left edge. A few moves later we get:

play_lightly4

For black, a win via E16 is just as valid as a win via J11.


Hopefully you could follow along with David’s examples here — as you can see, Twixt has a steep learning curve due to the sharp tactics involved, but the end result is a game with dynamic and exciting play.

Annotated Game — Zurround vs David Bush

This is a handicap game on a small grid, annotated by David Bush.  Red (Zurround) has to connect across 17 rows; Blue (David) has 18 columns to deal with.

A quick note on the move notation — for each move, we simply write the location of where the new peg was placed on the grid.  Since links are generally added automatically in most Twixt online clients or software you might use, it’s normally not necessary to specify which ones are added.  On occasion though you may need to change links around depending on the server — Game Center for example — so in those cases, if you need to understand the notation there is a quick guide on the page of interactive Twixt puzzles.

1. H9   2. H13

3. M11

handicap01

M11 is an excellent way for red to press his advantage. It makes many threats to connect to the top and to the bottom.

4. L8

5. J10   6. H5

handicap02

Blue is forced to open up a new front, but he may be able to use H13 later.

7. J6       8. K12

9. L13   10. M5

11. L7   12. N7

13. i4    14. J9

handicap03

Blue threatens to punch through along the top, at i7, or along the bottom, at L10. Red might be tempted here to play J8 which is a double linking move. But this does not answer both threats that blue is making.

handicap03a

I said that blue was threatening L10, and he is, but it would be a mistake to play there immediately.

handicap03b

Here red can win with H14.

handicap03c

Red threatens to double link at i12. We look at three variations here. The first is i11 G12 G10 F10:

handicap03c1

The second is i15 G12 G14 F14:

handicap03c2

and the third is G15 i12 i14 J14:

handicap03c3

So, instead of L10, blue should play at L14.

handicap03d

This is better than L10 because it still makes two threats to connect to the right, L10 or N13, and guards against red’s H14 threat. We will see how later in the game continuation. We return to the position after blue J9.

handicap03

In order to win here, red needs to play the same sort of trick that blue played with L14 in the previous variation. Blue used the space available on the bottom right. Red needs to use the space available on the left.

15. F8

handicap03e

Very good move. Red covers both of blue’s threats with a single move. The F8 group threatens to connect to the top in two ways, and to the bottom in two ways.

16. L14

handicap04

Red could have won here with F13.

handicap04a

One possible continuation is i7 F4 F12 E11:

handicap04b

It almost looks like blue could do a “pincer attack” here with E8. But it doesn’t quite work after E8 D7 G9 E9:

handicap04c

Returning to the game:

17. H14    18. G15

handicap05

Now blue is winning.

19. i12    20. i14

21. C14   22. D12

23. N14

handicap06

Red sets a trap. If 24. L10:

25. i14   26. K15   27. L15

handicap06a

But blue sidesteps the trap.

24. M16

25. D11    26. E10

27.Resign

handicap08

Next steps

From here, I suggest getting out there and playing some games!  After gaining some experience and putting these tips to the test, a good way to continue learning would be to check out David’s articles in Abstract Games magazine — in Issue 2, he provides the rules and a deeply-annotated game; in Issue 4, he covers basic tactical concepts and setups; and in Issue 7 he covers more details on how to battle for dominance in the corners.

There are several good options for playing Twixt online.  Probably chief among these is Little Golem, a correspondence game server which houses a dedicated Twixt community full of strong players, and the site supports the 30×30 and 48×48 variants as well.  Every game has a link next to it to enable you to analyse it on the Twixt Commentator website, which is also a convenient feature.

Note that Little Golem uses the TwixtPP rule set; PP stands for ‘pen and paper’, and these rules are actually the original rules for Twixt before the physical sets were produced.  In TwixtPP, your own legal links are placed automatically after each move by the server and are never deleted, and your links can cross over each other — but note that crossed links do not count as connected!  In practice, these minor rule differences don’t have a huge impact on play, but there are some rare situations where they do change things somewhat, so keep an eye out for those.

Also, this serves as a helpful reminder that you can play Twixt using pen and paper!  Just download and print some boards on a sheet of paper and draw your pegs and links using different-coloured pens or pencils.  This is a great way to try out the game without investing in a set.

You can also play Twixt on Richard’s PBEM Server — you’ll need to read the various FAQs and such to get started, but once you get past that you can play games graphically via the web interface.  This server supports games up to 40×40, and row handicaps of up to 18 rows.  Here the rules are those of the physical game, not Twixt PP; however, the server does automatically place legal links for you, which is helpful.

If you’d rather play Twixt in real time, igGameCenter is a great option, as mentioned above.  GameCenter supports row-handicapping as well, which is great for new players — David and I have played a few handicap games there and they were profoundly educational.  The board by default is drawn in a rather tiny resolution, but pressing Ctrl and +/-allows you to change the display size.  You can step back through your games afterward by clicking around in the move list, though analysing games in detail is probably best done by entering the moves into JTwixt on your own.  On the whole it’s a great place to play real-time games.

Summing Up

So that, in a nutshell, is Twixt.  I’m very much a newcomer to the game, and faced a trial-by-fire in my first matches by facing David right off the bat!  However, our games were not only educational, but also showed me that Twixt is challenging, filled with tension, and clearly can be a ‘lifestyle game’ just like Chess, Go, Havannah, or Hex.  I highly recommend trying it — the steep learning curve means it may not be for everyone, but if it is for you, there is a tonne of depth for you to discover and enjoy.

In future posts I’ll be covering some other interesting connection games with some unusual qualities: Onyx, a connection game played on an Archimedean tiling with captures; Gonnect, a connection game played using the rules of Go; and Slither, a recent invention combining placement and movement to generate shifting, snakelike connections across the board.  I’ll also be covering ConHex and the related meta-rules — rules that can modify almost any connection game — invented by Phil Bordelon.  Please look forward to those!

 

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Connection Games V: Side Stitch

We’re back looking at connection games again, and this time we’re going to cover a game invented in 2017 by Craig DuncanSide Stitch.  Side Stitch is a game reminiscent of Star and *Star, where players must make connections between groups touching key cells along the edges of the board.  Where Side Stitch differs from its predecessors is that it incorporates a recursive group-scoring mechanism that ensures there are no draws, rather than using a scoring penalty to encourage the formation of larger connected groups as in Star and *Star.

How to play Side Stitch

Side Stitch is played most frequently on hexhex boards (hexagonal boards tesselated with hexagons — examples below), on which the edges have coloured borders (although other shapes are possible — see the game’s image gallery on BGG for examples).  The number of colour-sides does not necessarily match the number of sides of the board!

The rules are very simple:

  1. Two players, Black and White, take it in turns to place a single stone of their colour on any empty hexagon on the board.  Once placed, stones do not move and are never removed.  Players may also pass their turn.  The game starts with the pie rule/swap rule.
  2. The game ends when both players pass in succession, or when the board is full.
  3. Once the game is over, the winner is determined by the scores for the players’ groups.  Each connected group of same-colour stones gives a score equal to the number of colour-sides that group touches (cells adjacent to two colour-sides count as touching both of them).  Each player finds their highest-scoring group, and the player with the highest-scoring group wins.  If both players have the same score at that point, then they compare second-highest-scoring group, then third-highest, and so on.  Draws are not possible in Side Stitch.

Here are some sample boards I made in Adobe Illustrator based on Craig Duncan’s designs, available for download on BGG:

Side Stitch 7-9-notation-01

Side Stitch hexhex-7 board with 9 colour-sides.

Side Stitch 8-7 big borders-01

Side Stitch hexhex-8 board with 7 colour-sides.  This is Craig Duncan’s pick for the ‘standard’ Side Stitch board, as he feels the 169 hexes allow for a suitably complex game without it overstaying its welcome.

Side Stitch 10-01

Side Stitch hexhex-10 board with 9 colour-sides.

From these sample boards you can see that Side Stitch plays well on wide variety of board shapes and sizes, and with different numbers of colour-sides.  The colour-sides also give the boards a lively and appealing visual aspect.  Craig Duncan recommends the hexhex-8 board with 7 colours-sides as the ‘standard’ Side Stitch board; I tend to agree with him that this board allows for deep and challenging play without dragging on too long.  Having said that the hexhex-10/9-colour board allows for a bit more of strategic battle, and to me is equally as good as the standard board.

The recursive group-scoring mechanism — comparing highest-scoring groups first, then second-highest, and so on until any ties are broken — has appeared in a few recent connection games and related titles, most notably Nick Bentley’s highly successful Catchup (easily my favourite game of his at the moment).  This mechanism works particularly well in Side Stitch — draws are impossible and the winner is very easy to determine.  In combination with the board’s brightly-coloured sides, it makes a strategically and tactically complex game highly readable in play — following who’s ahead is very straightforward.  As a whole, Side Stitch is a fun, elegant and fundamentally flexible game that scales really well.

 

Side Stitch in play

Despite its simplicity, players discover very quickly that Side Stitch has enormous depth and variety.  As players attempt to stitch the colour-sides together to form the highest-scoring group, they’ll need to pay equal attention to interfering with their opponent’s plans as well.  The need to connect widely ensures that play spans the entire board surface, and strategic concerns remain paramount even on smaller boards.

Here’s a sample game, one of my early attempts against Ai Ai’s MCTS player on the hexhex-7/9-sided board:

sidestitch9-loss1-end

The AI is playing Black here, and won with a board-spanning group in the centre connected to five colour-sides.  As this was an early attempt at the game, I was too wrapped up in my own attempts to connect in the opening phase, and failed to counteract Black’s efforts to split my stones in two.  Here’s a GIF so you can see my shame step-by-step:

sidestitch9-loss1-num

After several more losses, I took a game from the AI on the hexhex-8/7-sided board.  By this time I’d learned how to balance my attack and defence obligations more appropriately and to manoeuvre a bit more cleverly across the board.  The AI (Black) resigned in this position:

sidestitch8-win1-end

You can see that Black made a valiant, and ultimately successful, effort to block me from the left side of the board entirely.  However, I was able to extend all the way to the top-right corner, which together with the connections on the right and bottom netted me a group scoring 5 points — an insurmountable margin for Black.  Here’s a GIF of the full game:

sidestitch8-win1-num

Now this game is still young, and I’m by no means an expert myself, so it’s difficult to give detailed tactical and strategic advice.  But hopefully these sample games can give you some idea of how Side Stitch feels in actual play.  For me it’s a standout amongst the many recent connection games — it’s easy to understand but affords some very intricate play.  The colourful boards are really appealing, too, and so far the game retains its character and excitement on all the boards I’ve tried.

At a tactical level, connection game basics from Hex et al. will serve you well here; for strategic considerations, you can take some inspiration from games like Star and Starweb.  What’s key in Side Stitch, as in other connect-key-cells games, is to impede your opponent’s progress as well as furthering your own connections.  You also have to keep in mind the recursive scoring mechanism — if you and your opponent are fighting a close battle, then your second- or third-best group may well decide the game!  So don’t forget to develop additional scoring groups, in case the board situation may require a tie-break with your lesser groups.

 

Side Stitch 6

In response to thread on BGG, Side Stitch designer Craig Duncan designed a way to play Side Stitch using the six sides of the hexhex board, rather than having a different number of colour-sides.  In order to keep the play the same and avoid draws the board ends up being a bit different:

side-stitch-6-v1

The rules of Side Stitch 6 are the same as in normal Side Stitch, except that the missing corner cells obviously aren’t playable, and each player starts with stones already in contact with each of the six colours.

Personally I’d rather just play regular Side Stitch and try lots of interesting colour combos, but it’s nice that the game still holds together with six sides or other even numbers of sides, with some small adjustments.

IMPORTANT UPDATE: Side Stitch is now playable at the Gorrion Server!  Here’s how the game looks over there — note that scoring is not yet implemented so players have to do that on their own.  So far we have the hexhex-8 board with 7 colour-sides available (Craig’s standard board).

side-stitch-gorrion1

UPDATE 2: Side Stitch 10 — hexhex-10 board with 9 colour-sides — is now also available on Gorrion!

gorrion-side-stitch-10

 

Exo-Hex

The discussion on Side Stitch 6 eventually lead to the development of a sister game, Exo-Hex.  Exo-Hex takes the next logical step from Side Stitch 6 and eliminates the colour-sides entirely.  Instead, black and white stones are placed outside the boundary of the board — these are called ‘exo-stones’ — and players compete to build groups connected to the largest number of exo-stones.  The win condition and scoring mechanism are the same as in Side Stitch.  The result looks like this:

exo-hex-7

This new arrangement creates some new wrinkles — the sides are no longer neutral, but are already colonised by pieces of both players.  Also, since the sides consist of stones themselves, the sides are connective — in other words, a chain of stones coming in one end of a given side is still connected to a chain of stones coming out the other end.

Speaking personally, I’d still rather play Side Stitch — it has a level of personality and flexibility/extensibility that Exo-Hex doesn’t.  But as a consequence of this more focussed design, Exo-Hex is easily playable with any standard hexhex board and two colours of stones, and it’s elegantly simple.

 

Iris

Our last game of today is Iris, another 2019 invention from Craig Duncan with links to elements of Side Stitch.  Iris also has a colourful visual presentation and uses recursive group scoring, but uses a different movement protocol.

iris-game-1

An Iris sample game — check the game’s image gallery for more of Craig’s attractive board designs

Iris works like this:

  1. Two players, Black and White, take it in turns to place stones of their colour on the board.  Black goes first, and in their first turn may place one stone on any grey interior cell of the board.  After that, players may place two stones of their colour on the board subject to these restrictions:
    1. If a stone is placed on a coloured cell on the outer rim of the board, the second stone must be placed on the corresponding same-coloured cell on the opposite side of the board.
    2. If a stone is placed on an empty grey cell, the second may be placed on any non-adjacent grey cell.  If no non-adjacent cells are available, the second stone may not be placed.
  2. The game ends when both players pass, or the board is full.  Then players score their groups of same-coloured stones; the score of a group is equal to the number of coloured stones included in that group.  The highest-scoring group wins, and the scoring is recursive — if the highest-scoring groups have equal values, then we compare the second-highest, and so on.

I haven’t yet had the pleasure of playing Iris, but the prospect of a connect-the-key-cells game with two moves per turn (this is known as the 122* move protocol) is quite appealing.  The additional move would allow for some complex threats to be made and answered during play, and might further encourage the players to attempt adventurous cross-board connections.  A nice side-effect of the 122* protocol is that the pie rule isn’t necessary; the first player’s single placement at the start balances out the first-move advantage.

 

Summing Up

Side Stitch and its kin here show us that the design space surrounding the Star/Starweb connect-the-key-cells concept is rich with possibilities.  Side Stitch’s adoption of the colour-sides and recursive group scoring gives it a distinct character from its ancestors, and in play it shines as one of the better connection games I’ve played in recent years.  Exo-Hex and Iris are a bit more focussed in design, which has pluses and minuses — of the two, Iris stands out as having some interesting potential.  The 122* move protocol with placement restrictions adds an interesting wrinkle to this sub-genre of games.

All told, Craig Duncan’s had a productive couple of years!  Out of the three Side Stitch is clearly my favourite design, but if the others become playable via Ai Ai or other venues then that may change.  For now I think Side Stitch offers personality, playability and flexibility, and it’s certainly made it to the ranks of games for which I plan to print a mat and encourage others to play.

Next time, we’re going down a somewhat different route.  I’ll be covering a single game, the classic Twixt, in significantly more detail than the other games I’ve presented here.  This will be possible thanks to David Bush, three-time Mind Sports Olympiad Champion in Twixt, who has not only sent me fantastic content for that post but has given me a Twixt trail-by-fire in some very challenging games.  So do look forward to that post — hopefully you’ll come to the end of it packed with Twixt knowledge and ready for the tactical challenges the game has to offer.

 

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Connection Games IV: Unlur

I promised last time to cover two of my favourite connection games, Unlur and Side Stitch , but you may notice the title of this post only mentions Unlur.  I should clarify that my plans haven’t changed as a whole, I’ve just decided to devote an entire post to Unlur instead of covering both games at once.  Unlur is a deep and challenging game, so it deserves a bit of explanation — and if I cover Side Stitch separately as well, I can also cover a couple of related games by the same designer (Craig Duncan).

Unlur came about as a result of a game design contest in the Abstract Games magazine back in 2002 — the Unequal Forces Design Competition.  The competition challenged designers to create games where the two sides are asymmetric — having different goals and/or different tools with which to achieve the game’s win condition. Designer Jorge Gomez Arrausi won by creating Unlur, a game that took on a very difficult design challenge: how do you create a connection game where the players have unequal goals, yet the game remains balanced?

The Rules

As with most connection games, the rules of Unlur are appealingly simple, but the elegant rules enable remarkable complexity to emerge in play.  The first phase of the game, the contract phase, is particularly unique in Unlur, so after introducing the concept here I’ll illustrate how it works in practice with some brief discussion of several real games.

A game of Unlur is played on a hexagonal board tesselated with hexagons —  the classic ‘hexhex’ board we’ve seen a few times now.  The designer originally recommended playing on a hexhex-6 board, but hexhex-8 is more common — for a deeper and more subtle contest, try hexhex-10 or larger.   The game works like this:

  1. Two players, Black and White, compete to form connections between different sides of the board:
    • White wins if they connect two opposite sides of the board
    • Black wins if they connect three non-adjacent sides (corner cells are considered part of both sides to which they are adjacent)
    • If either player achieves the other player’s goal without simultaneously achieving their own, they lose the game immediately
  2. Black’s goal to connect three sides is significantly harder than White’s goal, so a game of Unlur is structured so that the players balance the game themselves before they start playing in earnest.  At the start of the game, players are not assigned colours — instead they begin with the contract phase.  In this phase, the two players take it in turns to place a single black stone on any empty hex that is not on the outer edge of the board.  When one player judges that Black has enough stones in the right positions on the board to give them an equal chance against White, they may pass their turn — from that point they play Black, and the other player is White.
  3. White then makes the next move by placing a White stone on any empty hex, and the players then take it in turns to place a single stone of their colour on the board.

Here’s the final position for a real game of Unlur on a hexhex-8 board played on Richard’s PBEM Server: unlur-8-example

Black won this game by resignation — White gave up because Black’s three stones on the bottom right of the board completely cut off White’s attempt to connect the top and bottom sides, and also ensure an unstoppable connection for Black.  Ultimately Black will win by connecting the bottom right corner and top left corner to the bottom left side — remember that corner cells count as part of both sides they’re adjacent to, so Black will achieve their goal of connecting three non-adjacent sides.

The genius of Unlur lies in the contract phase.  Essentially the contract is somewhat like an extended form of the pie rule used in many other games, except here players are not assigned colours initially and have complete freedom to decide at what point Black has equal chances.  Since neither player has chosen a side at this point, both are invested in making sure that the board is equal at the start, so both will add stones in such a way as to ensure whoever elects to pass and take Black will be competitive but not dominant.  The contract phase is of course hugely important to the ultimate outcome of the game, and the completely open nature of it means that opening play in Unlur is both unusual and extremely varied.

The rule enforcing a loss if either player achieves the other’s win condition serves to ensure that draws are impossible in Unlur.  In practice this rule affects Black more than White — after all, White’s goal is more economical in terms of stone placement, so it’s less likely they will end up forming Black’s more difficult connective goal before achieving their own.

 

The contract phase in action

The contract phase is not only ingenious, it’s also complex — how do we decide when Black as equal chances?  What sort of moves for Black should we play to ensure equal chances without unbalancing the game?

There are basic rules of thumb we can infer from our experiences with other connection games: the centre of the board is very valuable, so central stones for Black are strong in the contract phase; and conversely, stones closer to the edges of the board are weaker.  So as a starting point, we can say that a contract with several central stones for Black would be quite strong, while a contract consisting only of stones close to the edge would require more stones to be placed before we’d consider passing.

The designer adds to this that stones that are widely dispersed are more powerful than stones placed closely together.  This often leads to players cautiously adding more stones for Black adjacent to already-placed stones — this still increases Black’s chances but changes the position less drastically than placing stones elsewhere.

Even with these basic ideas in place, judging when to pass in Unlur is difficult, and our decision will have to change depending on the size of the board — on larger boards, Black would need a larger contract to have equal winning chances.  Let’s take a look at a few example games on different board sizes, and see how different players have addressed the contract phase in actual play.

First we’ll look at a tournament game played on a hexhex-8 board in 2006 on Richard’s PBEM Server.  Black ultimately won this game, and the contract certainly proved important in this case — here’s the game position when the winning player chose to pass and take Black:

unlur-8-diag-contract

 

In this game the contract consists of just six moves for Black — given that the designer’s analysis on the smaller hexhex-6 board suggested that up to ten stones for Black could still constitute a fair contract, we might conclude that Black’s contract was too weak here.  However, remember our rules of thumb — Black’s stones are close to the edge, but also widely dispersed, so they provide a framework for later connections across the board.  The stones are also close to several corners, which count as part of either side they’re adjacent to, which again is helpful for Black.

Black’s win in this game made very good use of these contract stones, as we can see:

unlur-8-diag-end

Note that all of the contract stones save the stone on H11 played an important role in subsequent play.  The two stones in the bottom left were ultimately blocked by White, but Black nevertheless slipped through the centre to connect the contract stones on the left and upper right with the bottom of the board.  So in this case Black’s judgement of the contract proved correct — the number of stones was small, but they formed a framework for connection that Black could exploit well enough to take the win.

Now let’s jump up to a hexhex-9 game and see how the contract phase evolved:

unlur-9-diag-contract

Now this contract seems even more risky than the last one!  The winning player took the contract after just three moves — this despite playing on a hexhex-9 board which has 217 hexes, far more than the 169 in the hexhex-8 board of the previous game.  Given our rules of thumb we can see that these moves are quite powerful for Black, however; two of them are quite central, and while the stones aren’t widely dispersed they do provide good coverage of the top and top-right of the board.

As it happens, Black was able to construct a nice win here:

unlur-9-diag-end

Note that the two central stones from the contract phase formed a crucial part of the winning player’s connection — in fact the winning Y-shaped configuration spreads out directly from those two stones.  Clearly more centrally-placed stones are quite powerful for Black, and can enable Black to form a strong core for a board-spanning connection.

I’d argue though that taking this contract after just 3 moves was still quite a risky play — after all, the board is large and there was still ample room for White to manoeuvre and possibly isolate those stones.  We should remember though that the contract is only the first stage of the game, and skilful play can still make up for a less-powerful contract.

In that sense the contract phase in Unlur could also function as an interesting way to balance the game between two players of very different skill levels.  I suspect with some detailed analysis we’d be able to develop a reasonably granular system for constructing contracts that help bridge skill gaps between players — perhaps by constructing some pre-set contract placements tailored for different skill levels, or by giving one player additional stones to place in the contract phase.  As far as I know this hasn’t really been investigated in detail, but I’d be interested to see some testing of possible handicap play rules.

So far we’ve seen a couple of relatively small contracts — let’s take a look at some more generous ones.  First we’ll jump up in size again to this game on a hexhex-10 board, where Black takes a contract four times larger than the last one we studied:

unlur-10-diag-contract

Here Black took the contract after 12 moves.  The distribution of stones suggests both players were playing carefully, looking for a balanced and relatively straightforward position — all 12 stones are placed near to the edge of the board, and we see two large clusters of adjacent stones, which as we know are less impactful on the position than more widely-scattered ones.  Given the size of the board — 271 hexes, much bigger than the previous game’s 217 — 12 stones in this kind of configuration seems a reasonably fair contract, giving Black a strong framework around the edges but leaving the centre open.  We might expect play to focus on that open centre as Black seeks to connect these disparate islands of stones, and White tries to wind their way through the maze to build their own connection.

This ends up being pretty accurate, as we can see in the final position:

unlur-10-diag-end

Black ends up building several strong walls around the centre, blocking White from easily connecting through the middle of the board.  White resigned at this point, as it’s clear Black can stop them from connecting to the top, while Black’s structure ensures unstoppable connection between the bottom, right and top sides.  In the end Black played cleverly here and utilised the strong points of this contract well — the contract stones helped restrict White’s playable territory along the edges, and Black’s subsequent play largely blocked them out of the centre.

Finally let’s take a look at another well-balanced contract, this time on a rather gargantuan hexhex-11 board (331 hexes):

unlur-11-diag-contract

Here Black took the contract after 15 stones were placed.  Note again how many of the stones are clustered together, reducing the overall impact of each placement on the position.  However in this case we have a stone placed right in the centre of the board, which is certainly helpful for Black.  Given the size of the board and the fact that there’s just one central stone, 15 stones seems like a reasonably fair contract for Black.

The resulting game, another Black win, develops in an interesting way.  In issue 12 of Abstract Games, the designer of Unlur explores this kind of opening position and a resulting position called the arrow opening, which we can see in supersized form in this game after the above contract:

unlur-11-diag-end

In this arrow game, White is in quite an unfortunate bind — their long wedge of stones on the bottom-right is completely hemmed in.  If we were speaking in Hex terms, we’d say that nearly all of White’s stones are dead — unable to take part in any winning connection.  Black has blocked the corner at U11 and constructed a vast wall as well, making a White connection between the lower-left side and the upper-right completely impossible.  White’s attempt to snake around the right side to connect to the top is easily stymied by Black using the group of stones on and around D14, so White’s position is utterly hopeless.  Black can easily win by connecting to the upper-right side — note this also forms a line, but since Black already connected the bottom (using the corner cell) and the upper-left, Black’s stones would form a 3-way Y connection at the same time, securing the win.

Hopefully these few examples can serve as a useful preview of what a sound contract for Black can look like in Unlur on some of the possible board sizes.   The number of possible contracts on any given board size is absolutely enormous — contract length can vary a lot, as we’ve seen, as well as the positions of the stones.  In the face of all this variability,  a few rules of thumb and experience are the best we can hope for; there are so many ways the contract phase can evolve that set opening sequences are not particularly useful.  Besides, your set opening can easily go awry if your opponent decides to go another way — after all, you’re building the contract together, not separately!

After the contract phase, you’ll find yourself using some of the same basic concepts you might use in other connection games like Hex or Y — bridges and so forth.  However Unlur is significantly different in one very important aspect: your own stones are never a liability in Hex or Y, but they definitely can be in Unlur!  You lose the game if you form the opponent’s connection before your own, so having poorly-placed stones scattered around the board can make this outcome more likely.

During the middle- and end-game of Unlur, it’s also worth keeping in mind some key configurations that ensure a win for one player or the other:

Unlur-config1-edited

In the above pattern, Black completely controls three sides of the board.  In this configuration White cannot win — White would need to connect to one of the sides controlled by Black.  White will lose either when Black successfully connects or when they are eventually forced to make a foreign connection.

unlur-config2-edited

When White completely controls two opposite sides, Black is completely lost.  In order to connect three non-adjacent sides, Black would need to use one of White’s controlled sides, which is impossible.  Meanwhile, White still has several different ways to make a winning connection.unlur-config3-edited

This pattern is another one that hands a certain win to White.  White can still connect to the top to form a winning line, but Black can’t break through — he can only form a losing line in the attempt.

During the game, watch out for your opponent working toward these configurations — don’t let them get away with it!  We can easily forget the ‘foreign connection’ rule and end up in a situation where we’ve unwittingly entered a board position where the foreign connection is the only one available to us.

 

Resources and where to play

Despite being a relatively well-known connection game and widely respected for its elegance and uniqueness, strategic advice on Unlur is rather hard to come by.  Your first stop should be issues 11 and 12 of Abstract Games — the game is introduced in issue 11, and the designer provides some background on his design decisions and some strategic advice in issue 12.  Note that he only covers hexhex-6 boards, as he felt that larger boards were too complex:

“…Unlur over a board with eight cells per side becomes very complex and difficult to understand, so now we prefer to play on a board with six cells per side.”

However, since those articles were published many players have come to prefer larger sizes, because there is greater scope for strategic intrigue.  I personally prefer larger boards as well, partially because the contract phase takes up a bit less of the overall play time on a larger board, which to me feels a bit better balanced in terms of the playing experience.

From there, you can check the archived version of the designer’s website for further tips, but unfortunately none of the images appear to work anymore.  Other than that I can’t really find any detailed strategic discussion anywhere, which is quite a shame.

That being the case, the best way to learn is to try playing some games.  Unlur is well-known enough that there are a few options for online play: Gorrion (supports hexhex-8, 10 and 12), Richard’s PBM Server (supports from hexhex-4 all the way up to 13!), igGameCenter (supports hexhex-8 and 10), and Ludoteka (supports hexhex-6 and 8).  Unfortunately all these servers are somewhat lacking in Unlur activity, but I’m sure you could rustle up a game or two via BoardGameGeek… or simply contact me if you want to arrange a few!

If you want to play in real life, I’ve made some Unlur boards in a range of sizes — hexhex-6, 7, 8, 10 and 12 — which are directly derived from the original Unlur hexhex-6 board offered in Abstract Games magazine.  I posted them on BoardGameGeek with permission from Kerry Handscomb of Abstract Games.  There are two versions — one with the original muted bronze board colour and grey background, the other with a white background and lighter board colour.  Both are in PDF format and look great printed out on a gaming mat — you can see my own neoprene-printed version below!

Summing up

Unlur is a game of genuine ingenuity, and it offers unique wrinkles you won’t find in any other connection game.  The contract phase is a fantastic addition, artfully accomplishing the difficult design goal of a balanced asymmetric connection game.  Finally, it’s fun — the contract phase is tense, forcing you to constantly second-guess your opponent and think carefully about each stone and how it will affect the coming game; and the subsequent connection battle feels even more consequential than in other games, given that your own misplaced stones can come back to bite you, potentially forcing you to make your opponent’s connection and lose the game.  I give this game my highest recommendation and hope some of you might consider giving it a try.

Related Games

Before I move on I’d be remiss not to mention Cross, Cameron Browne’s connection game inspired by Unlur.   Cross is also a connection game played on a hexhex board, but here there is no contract phase — instead, players both are striving to connect three non-adjacent sides of the board, and either player will lose if they make a line connecting two opposite sides of the board.  The game plays very differently than Unlur, but the shared element of the Y-connection wins/line connection loses dynamic leads to some tense situations, much like the middle/late-game of Unlur.

Conveniently, you can buy a physical Cross set with a hexhex-7 board from Nestor Games — and the components are generic you can play Unlur on that set too if you want!  Nestor also offers hexhex-8 and hexhex-10 boards via the games Iqishiqi and Omega respectively, if you want to play larger games.  Cross is also playable on Richard’s PBEM Server.

While I’m here I should also mention Coil — an intriguing game by Nick Bentley that adopts Unlur’s contract phase mechanism.   In Coil, players start with a contract phase as in Unlur, except the board starts with black stones in each corner cell, and stones placed during this phase cannot be placed adjacent to one another.  Once someone passes and takes the contract as Black, that player must then try to form a loop of Black stones (a loop being defined here the same way as in Havannah), while White tries to prevent the loop from being formed.  If Black forms a loop, they win; if the board fills up without a Black loop, White wins.  Coil is an interesting take on the asymmetric connection game, and ends up feeling quite different from Unlur.  Again it’s playable on any hexhex board with black and white stones, so definitely give it a try after your Unlur games!

Nick Bentley also designed another game with a loop-formation win condition and an Unlur-esque contract phase — Bobina, where players bid not with the black stones but instead with grey neutral stones that can help either player form a winning loop.  The concept is very clever but a bit hard to explain briefly here — I’d recommend you go have a read of Nick’s blog post to get a clear picture of it.  This is another interesting take on the contract phase, and definitely worth a try if that aspect of Unlur appeals to you.  I have to say I slightly prefer Coil due to the simplicity of that game and the asymmetric aspect, but Bobina does offer a unique twist with the neutral stone element.

That’s it for our in-depth look at Unlur — next time I’ll cover Side Stitch and sister games Exo-Hex and Iris.

 

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Connection Games III: Havannah and Starweb

In keeping with Part II, today I’m going to introduce two games by one designer — Christian Freeling, who maintains an invaluable website full of his creations including versions playable in your browser.   Christian has invented a tonne of well-regarded games over the years, and he has his own opinions on the most essential ones — namely Grand Chess, Dameo, Emergo, Sygo, Symple and Storisende.  Although I’m not sure I can agree with most of them, personally speaking — that list is mostly games I certainly admire, design-wise, but don’t particularly enjoy playing.

However, there are two of his games that I find completely, indisputably brilliant:  Havannah and Starweb.  Both are fantastic additions to the connection game family.

Havannah

Havannah is a connection game that offers a completely unique take on the genre.  Connection games are typically characterised by a sense of absolute clarity — the goal is simple, singular, and direct.  Connect a thing to other things, and there you go.  But in Havannah, players can win in three different ways — and to play well, you need to threaten to do all of them and defend against all of them simultaneously.  The consequence is a game of intense depth and richness, and substantial challenge.

Here’s the basics:

  1. Two players, one with black stones and one with white, play Havannah on a hexagonal board tessellated with hexagons (known as a ‘hexhex’ board).  The commercial Havannah release used a hexhex board with 8 hexes on a side (169 playable hexes), but Freeling considers a hexhex-10 board to be ideal (271 playable hexes).
  2. The game starts with the swap/pie rule.
  3. Each turn, a player places one stone of their colour on any empty space on the board.  Once placed, stones do not move and are never removed.
  4. A player wins when they achieve one of the following configurations (these examples are from real games on Little Golem) —

ring — a chain of pieces that completely surrounds at least one hex, which can be empty or occupied (by opposing stones or your own):

havannah-bigring1

Rings can get quite elaborate — can you see how White’s convoluted ring formation here?

havannah-ring1

Rings can also be tiny and enclose just one hex!  These are easier to spot so it can hurt when you lose this way….

fork — a chain of stones connecting three non-corner hexes on three different sides of the board:

havannah-fork1

Black completes a fork here.  Note that it includes a corner hex, at the bottom, but also includes a non-corner one there too, so it still works!

havannah-elaboratefork

A rather impressively labyrinthine fork here from Black.  A clever win from what looks like a hard-fought game.

A bridge — a chain of stones connecting two corner hexagons:

havannah-bridgeproper1

White constructs a fairly convoluted bridge here from the top-right corner to the bottom corner

As you can see already, Havannah puts a lot on your plate as a player.  The rules are hardly any more complicated than any other connection game, but the objectives are many and varied.  The consequence of this is that at every turn you must be aware of the many possible implications of your opponent’s stones, and you have to learn to catch the signs of key strategic and tactical threats.

In fact the game is so strategically rich that in 2002 Christian Freeling instituted an AI challenge, betting €1000 that no computer could beat him even one game out of 10 on a hexhex-10 board within a decade.  Predictably, he lost that challenge in 2012 and lost 3 games of his ten-game match against the machines.

Now one might feel disappointed somehow when computer players surpass humans in games, but honestly having superhuman AI for a newer game is a good thing — it accelerates the decades- or centuries-long process we normally need to really probe how our games hold up at a high level of play.  That aside, to be fair to Christian Freeling, his game lasted nearly the full decade; these days, if anyone with some decent computing power is paying attention, any game would be lucky to last a few months.  Especially now that AI doesn’t even need to know the rules first to master a game!

Basic Havannah Tips

Havannah, even more than other connection games, really comes alive once you’re armed with a few key strategic and tactical concepts.  I’m by no means an expert here — at the end of this section I’ll link you to some people that are — but there’s a few tips I can offer to get you started:

  1. The game plays kind of like a combo of Go and Hex — a certain Go feel is apparent in how important whole-board strategic vision is, and that groups of stones can be ‘alive’ or ‘dead’ depending on their capability to form part of an attacking threat.  The Hex side manifests in the moment-to-moment tactics and the importance virtual connections (bridges, in Hex terms) between stones.
  2. Perhaps the most important strategic concept to learn is the frame — a set of stones forming the backbone of an unbreakable winning formation, regardless of the opponent’s response.  Check the guides I link below for some examples, and keep an eye out for your opponent threatening to make a frame!
  3. The one-hex ring enclosure — the mill — is a really important tool in Havannah.  Rarely will you beat an experienced opponent that way, but building a mill can force a response from your opponent, gaining you initiative — and can interfere with their plans for their own stones, as well.  Conversely, it’s important to learn how to defend against mill threats so you don’t fall prey to the same outcomes.
  4. Board size matters!  On smaller boards, bridges and forks are powerful.  On larger boards (hexhex-10 and up), bridges and forks are harder to build and rings become somewhat more prominent.
  5. Draws are possible in Havannah — but just barely.  Out of tens of thousands of online games, there are single-digit numbers of draws that have ever happened!  Therefore, don’t think an attempt at a drawing strategy will save you when things go bad — it’s extremely unlikely to work!

 

Havannah frames

An example of a ring frame (Black) and a fork frame (White)

To really dig into the complexities of Havannah, I strongly recommend the brief but comprehensive guide by David Ploog, available in PDF format here (and please see his other amazing guides for other games in the BGG thread here), which covers all the key concepts and includes numerous examples and some problems to test your comprehension.

For a bit of discussion and strategic and tactical guidance for Havannah from the creator himself, do check Christian Freeling’s Havannah website, and his articles in issues 14, 15 and 16 of Abstract Games Magazine (that link takes you to their back-issue archives).

Finally, when you feel up to the challenge, you can play Havannah via Stephen Tavener’s Ai Ai program, the Mindsports website, on Little Golem, Richard’s PBEM Server, igGameCenter, and probably other places too!  There’s a physical version of Havannah published by Ravensburger in 1981 that goes for very little on Ebay, but that only has a hexhex-8 board — for larger ones you’ll need to print something up yourself or repurpose another set, like Omega from Nestor Games.

While I’ve been on strike, my wife has helped me to learn Adobe Illustrator so I could make some nice hexhex-10 and hexhex-12 boards usable for Havannah and numerous other games.  The final results are available in three colour schemes from the BoardGameGeek Havannah files section.  These are sized for printing on 25 inch by 25 inch neoprene playmats, which are a popular way to get sturdy game boards made these days.  If you printed them on mats of that size you can use standard 22mm Go stones on these boards.

I also made hexhex boards of size 7, 8, 10, 11, and 12 in the style of the board used on Little Golem, which is probably the most popular place to play Havannah.  I like the random splash of colours across the hex grid, so I decided to create a range of print-and-play boards in that style.  You can find these boards at my BGG filepage for Havannah along with the other versions.

hexhex-10_RED-01

Hexhex-10 board, with highlighted borders to allow players to use this one board as a hexhex-9, 8, 7, etc. as well.  Two other colour schemes are available on BGG, too.

hexhex-12_LG style-01

Hexhex-12 board in Little Golem style.  I really am proud of this one, as it took some doing to replicate that colour pattern. 

Laika-hexhex10

Showing off how the game works on my neoprene-printed hexhex-10 Havannah board.  My dog Laika is fascinated.

However you go about playing it, Havannah is an absolute gem among the connection games.  It’s tactical and strategic, mind-bending, and always enticing to play.  If there were any justice in the world it’d be getting played by millions of people like Chess and Go, but alas, we’ve got to dig up players the old-fashioned way.  But Havannah’s worth the trouble.

 

Starweb

One thing you’ll notice about Christian Freeling if you start following developments in the abstract strategy games community is that he has claimed he was retiring from game design about 100 times, yet he always comes back.  Starweb appeared during one of these ephemeral retirements — he says the game came to his mind suddenly, basically fully-formed almost out of nowhere.  Lucky for us that it did, as in my opinion it’s another masterpiece.

Starweb is a clear descendant of Star/*Star, being a connection game that incentivises connecting certain key points on the board with as few groups of stones as possible.  What makes Starweb stand out is both the shape of the board, which creates 18 key corner hexes that drive the gameplay, and the triangular scoring mechanism.

Starweb’s simple and elegant rules lead to board-spanning strategic play, in some ways reminiscent of Havannah.  Here’s what the standard board looks like:

starweb-regular-01

Starweb standard board (dubbed size 10 in Ai Ai).  It’s a hexhex-7 board with six added chunks of 15 hexes on each side, giving us 217 playable hexes in total, and 18 corner hexes (highlighted in brown).  And yes, that is the font from Star Trek — bonus nerd points if you know what language that is underneath the Trek-style logo!

Play is appealingly simple, although the scoring mechanism takes a moment to sink in:

  1. Two players, Black and White, play on the standard Starweb board or one of its smaller variants.  The board starts empty.
  2. Play starts with the swap/pie rule.
  3. Each turn, a player places one stone of their colour on any empty hex on the board.  Once placed, stones never move and are never removed.  Players may also pass their turn and not place a stone.
  4. The game ends when both players pass in succession.
  5. Once the game ends, players calculate their score as follows:
    1. Players identify each group of their stones that contains at least one corner cell (a ‘group’ is a connected bunch of like-coloured stones)
    2. The score for a group containing n corners is the sum of n and all positive integers less than n.  In other words, a group containing 1 corner is worth 1 point; 2 corners = 2 + 1 = 3 points; 3 corners = 3 + 2 + 1 = 6 points; 4 corners = 4 + 3 + 2 + 1 = 10 points; and so on.
    3. The player with the highest score wins.  In the event of a tied score, the player who placed the second stone wins.

So, to win Starweb, you have to occupy corner cells and connect those corners together into united groups of stones to score more points — the more corners in your group, the more points you score.  At the start of the game the players will normally go back and forth occupying corner cells, and from there proceed to wind their way across the board trying to connect them together.  This leads to dense, complicated webs of connected stones — hence the name Starweb!

I have to admit I’m not a huge fan of the second-player-wins-draws rule, since there’s already a swap rule in place at the start — that reminds me of Armageddon Chess, where Black wins in the case of a draw, which is pretty widely disliked.  But the abstract games community generally seems very adamantly against draws, and designers tend to go to significant lengths to avoid them.  That seems somewhat strange to me, since that means the game is by definition unbalanced as one of the players will have a winning strategy with perfect play; I personally slightly prefer Havannah/Shogi scenarios where draws are possible but just quite rare.  In any case equal scores in Starweb are going to be pretty uncommon, so it’s not a big issue particularly, but the rule may influence your decision whether or not to swap your opponent’s opening move when going second.

Playing Starweb

The richness of Starweb becomes apparent once you discover that preventing your opponent’s connections between corners can be just as vital as connecting your own.  Early on Christian Freeling realised that a minority strategy — in which one player declines to take all the corners they could and instead works to invade the opponent’s territory and deny them connections — is quite viable.

Here’s an example game against AI on a small board that he posted on BoardGameGeek:

starweb-8-corners-small

You can see here that White (the AI) holds more corners (10 vs 8), but Black (Freeling) managed to cut several of them off, denying his opponent the ability to make big-scoring groups.  Meanwhile he was able to slice through the centre of the board, leading to a winning score despite holding less corners.

This game also shows off other nice properties of Starweb: the games tend to be intricate and long; and the game plays well even on much smaller boards.  The Starweb implementation in Ai Ai allows for boards even smaller than the above, and the game still holds up.  It’s definitely more fun on the normal-sized board though.

The minority strategy still works on the large board, too:

starweb-minority-strategy-large

After connecting stones 86 and 6 in the bottom right, Black will extend his lead by 5 more points. White is completely lost.

Freeling (Black) again takes less corners here, but manages to sprawl all the way across the board for a big-scoring connection.  White has no hope of catching up, as the AI’s largest groups are split down the middle by Black’s connection across the centre of the board, and the extra White corners elsewhere are completely walled off.

Through these sample games we can see that Starweb admits a variety of strategic approaches; when first learning the game we might think grabbing every corner is essential, but as we see above, denying your opponent scoring opportunities can compensate.  And by declining corners you can gain the initiative, exchanging turns you’d have spent on building a group for turns you can spend on attacking your opponent’s strategic goals.

At first the game might seem overly mathematical, in that counting corners and calculating scores seems so critical.  But in actual play that doesn’t really interfere; once corners are occupied, you don’t need to track them anymore, and that normally happens very early in the game.  Subsequently you just need to be aware of how many corners you need to connect to keep your opponent at bay.  So the numbers come into play when planning your approach to a particular early-game board situation, but after that you can focus mainly on tactics and trying to connect your groups and execute your plan.

For detailed and enlightening discussion on Starweb’s strategic complexities, you can check out the discussion from Freeling and others on BoardGameGeek.  That thread goes into more detail on the sample games I posted, and numerous others as well.  There’s also some useful discussion on the Arimaa Forums in this thread, starting at post #104, although sadly the image links are all broken now.  Starweb is still a young game, so as more people discover it perhaps we will see start to see guides on strategy and tactics on the level of those we can find for Havannah.

I highly recommend Starweb — you can play on Freeling’s MindSports site, or you can play against AI and human opponents on various board sizes via Stephen Tavener’s AiAi software of course.   In my opinion it’s an underrated gem, right up there with Havannah as one of the most strategically satisfying connection games.  It’s still early days for Starweb, as it was only developed in 2017, so hopefully as the years go by the game will develop the following it deserves.

Where next?

So, we’ve taken a look at the connection game titan Hex, the quirky and influential family of games by Craig Schensted/Ea Ea; and now two strategic masterpieces by Christian Freeling.  Already you could easily spend a lifetime exploring these games and never unlock all their secrets.

Of course that’s far from everything the genre has to offer!  Next time I’ll cover one more excellent connect-the-key-hexes game, Side Stitch, and then I’ll spend a fair bit of time talking about Unlur, an ingenious asymmetric connection game where the two players have different winning conditions.

 

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Connection Games II: Y, Poly-Y, Star and *Star

Welcome to part II of my series of posts about games, part of my mission to keep my brain busy while I’m on strike!

Moving on from the last post about Hex, this time we’re going to explore a whole series of connection games, each by the same designer and each a clear progression from the last.  By the time we get to the final game in the series, we’ll see one of the more complicated and sophisticated connection games out there.

The Game of Y

First though, let’s start with something simple.  In fact, this game is even simpler than Hex, which scarcely seems possible!  Recall that in Hex, each player has a slightly different goal — both seek to connect across the board, but each player is connecting different sides.

In the Game of Y, created by Craige Schensted (who later renamed himself Ea Ea) and Charles Titus in 1953, players have the same goal — to connect all three sides of a triangular board made of hexagons.  To sum it up:

  1. Players take turns placing one stone of their colour in any empty hexagon on the triangular board.  Once placed, stones do not move and are never removed.
  2. The first player to connect all three sides of the board wins.  Corner hexes count as part of both sides to which they are adjacent.

And that’s it!  Winning connections spanning the three sides look kind of like the letter Y, hence the name.  Just like Hex, Y cannot have draws, one player will always win eventually.  The first player has a winning advantage here, as well, so using the swap/pie rule is recommended to alleviate this.

Y is sometimes thought to be even more elemental than Hex, given the greater purity of the win condition.  In fact, Hex can be shown to be a special case of Y, but in practice the games are pretty distinct in terms of the tactics required.

Here’s a sample game I played against a simple AI on a triangular board 21 hexes on a side; I used Stephen Taverner’s excellent Ai Ai software that comes with a plethora of great connection games:

 

y-win-1

Y benefits from playing on a larger board, given the shorter distances between sides when compared to a Hex board.

One issue with Y is that, even more so than Hex, the centre hexes are very powerful.  Whichever player controls the centre is very likely to win.  Schensted and Titus developed a number of ideas for new boards that would reduce emphasis on the centre, and eventually the ‘official’ Y board became this interesting geodesic hemisphere:

y-17-curvedThis board reduces the connectivity of the central points, giving the sides and edges greater influence on play.  Some theorise however that on this board basically every first move should be swapped by the second player, although I don’t believe there’s any hard evidence that this is true.  Kadon Enterprises sells a lovely wooden version of this board, albeit smaller than the one above, with 91 points available for stone placement. 

UPDATE:  Phil Bordelon reports in the comments below that the Kadon Y board is so small that the game feels like a trivial first-player win!  So perhaps if you want to try this board shape, play the larger one on the Gorrion server, or print the larger pattern on a mat for face-to-face play.  David Bush also wrote to say that he believes the geodesic Y board can’t be balanced with just the pie rule, and given his serious pedigree in the connection games world I think I will take his word for it!  He also says that three-move equalisation can be a solution.  In this method, one player creates a position with two Black stones and one White, with White to move, and the other then decides whether to play White or Black.

Another alternative option to the geodesic Y board is known as Obtuse-Y.  In this version of the game we play on a hexagonal board tessellated with hexagons (a ‘hexhex’ board), with three pairs of sides marked — first player to connect all three of those marked sides is the winner.  I like this version of Y since a large board in this format is more compact than a gigantic triangle of hexes, and it’s easier to have a balanced game than on the geodesic board.  I made two boards for this version, which you can find on BoardGameGeek — a hexhex-10 (10 hexes on a side) and hexhex-12.

hexhex-10_Obtuse-Y-01

My hexhex-10 board for Obtuse-Y — connect all three colours to win!  There are 271 playable hexes on this board.

In any case, Y is another simple-yet-deep experience and highly recommended.  You can play against the AI using the Ai Ai software linked above, or against humans in real time via igGameCenter, or by correspondence on Richard’s PBEM Server.  The geodesic version is only playable on Gorrion — definitely give it a try.

Finally, I want to note that Y has a ‘Misère’ version, much like Hex, where you try to force the opponent to connect all three sides before you do.  This variant of Y is called ‘Y-Not’.  I just love that.

 

Mudcrack Y and Poly-Y

The next step in Y’s evolution came when Schensted and Titus published a gorgeous little book called Mudcrack Y and Poly-Y (you can still buy it from Kadon), which contained hundreds of strange hand-drawn boards for Y players.  They intended for players to use these boards by marking spaces with their chosen colour using coloured pencils.  These weird little boards seem totally different from the normal Y triangle or geodesic hemisphere, and yet turn out to be topologically equivalent.  Here’s a sample page:

mudcrack y1

A sample page of Mudcrack Y boards.  Print them out, grab a couple of coloured pencils and give them a go!

As part of their continued quest to improve on the Game of Y, this book also reveals Poly-Y, a follow-up game intended to be a further generalisation of Y:

  1. Players take turns placing a stone of their colour on any empty space on the board.  Once placed stones cannot move and are never removed.
  2. If a player’s stones connect two adjacent sides and a third non-adjacent side, that player controls the corner between the two adjacent sides.
  3. If a player controls a majority of the corners on the board, that player wins.

As you might have guessed, once again this game permits no draws (as long as you play on a board with an odd number of corners), so one player will always win.   The pie rule is used to mitigate the first-player advantage.

Wikipedia and BoardGameGeek claim there is no ‘official’ Poly-Y board, but this isn’t correct.  On the archived version of Craige/Ea Ea’s website you can find his summary of the history of Y/Poly-Y/Star/*Star, where he says this:

“Craige tried boards with more and more corners, 5, 7, 9, 15 … . At first it seemed that the more corners the better — there were more points to contest and a beautiful global strategic picture emerged. But as the number of corners increased, of necessity the length of the edges decreased. When the edges became too short it was found that it was too easy to make a Y touching 3 consecutive edges, thus “capturing” the middle edge and the two corners bounding it. This “edge capture” tended to make the game more tactical and local, focused on quick gains along the edge, thus losing the elegant global strategic flavor . So the strategic depth increased at first as the number of corners increased, but then decreased. Finally a board with 9 corners and 7 cells along each edge was chosen as the ideal balance….  Craige chose the 208 cell board with the 7-sided regions halfway to the center as the standard Poly-Y board.”

The same document has a picture of the standard board compared to two other candidates:

poly-y-board-official

The ‘standard’ Poly-Y board is in the centre.  The highlighted spaces on each board are the heptagons, required to allow the board to have 9 corners and still consist mostly of hexagons.

Here’s an example Poly-Y game won by Black on a board with 106 spaces and five corners — note here that the other player is Grey, and the yellow spaces are unoccupied:

poly-y-sample-game2

Black controls the corners on the left side, and has blocked Grey from catching up.

While Craige/Ea Ea endorses the 208-cell nonagon as the best Poly-Y board, in Mudcrack Y and Poly-Y they also state the game plays well on any board with the following characteristics:

  • Equal numbers of spaces along each side
  • Mostly six-sided board spaces
  • An odd number of sides (they prefer 5- and 9-sided boards)

Here’s sample 5-, 7- and 9-sided boards to print and play on:

poly-y-5-sided

5-sided Poly-Y board

poly-y-7-sided

7-sided Poly-Y board

poly-y-board9

9-sided Poly-Y board

 

Poly-Y is a clever game, and very deep; the win condition pushes players to extend their groups of stones all over the board, linking corners together through the centre to block the other player from securing their corners.  The oddly-shaped boards are also fun to play on, and give the game a certain quirky aesthetic appeal.  However, perhaps due to the rapid-fire iterations on Y produced by Schensted, Poly-Y never got the same level of recognition as Y itself.

 

Star

Schensted wasn’t quite done yet — far from it.  His next invention was Star, which ramped up the complexity of the scoring system from Poly-Y and created a game that pushes players to connect all over the board.  Star is another very deep game, and even on a small board presents a considerable challenge.

Star is played on a board of tessellated hexagons with uneven sides — in the sample small board below, you can see that three sides are five hexes long, and the other three are six hexes long; this ensures that there’s an uneven number of edge cells so that draws are impossible:

Star

A small board for Star with 75 hexes and 33 border cells.

Here’s how to play Star:

  1. Players take turns placing one stone of their colour on any empty hex.  Once placed, stones do not move and are never removed.
  2. A connected group of stones touching at least three of the dark partial hexes around the edge of the board is called a ‘star’.  Each star is worth two points less than the number of dark border hexes it touches.
  3. When both players pass or when the board is full, the player with the most points wins.
  4. As per usual, the pie rule is used to mitigate the first player advantage.

This may sound a bit opaque, but the basic gist is: form as many stars as you can, but connect them together to maximise your points.  The end result of a game of Star is an intricate web of connections snaking across the board for each player, attempting to connect and block simultaneously wherever possible.  Since the entire edge of the board is available for scoring, the whole board interior tends to come into play as well, and unlike most connection games the board tends to be nearly full when the game finishes.

Unfortunately, despite pretty much universal praise for this game it’s very difficult to find sample games of Star, so here’s the only one I could find from Cameron Browne’s book Connection Games — I can’t emphasise enough that this is a great book that you should definitely buy!

star-sample1

In this example, the edge scoring cells are marked by X’s rather than a border of partial hexagons.  Note that the completed game takes up nearly the entire board, and the pattern of connections formed is quite intricate even on this small playing area.

As with other connection games, playing on larger boards amps up the strategy.  I found these boards lurking around the Wayback Machine, do give them a try:

Star2

This board has 192 interior cells and 51 border cells.

Star3

This board has 243 interior cells and 57 border cells.

I liked these boards so much that I made a range of Star boards — sizes 8, 9, 10 and 12 (the number being the number of hexes on the longer sides).  I hope a few folks might print them out and give Star a try sometime.

Star-8_PURPLE-01

My size 8 Star board in purple

Unfortunately, despite the coolness of this game it’s been thoroughly overshadowed by its successor; Star does appear to be playable at Richard’s PBEM Server, albeit only with an ASCII interface.

 

*Star

Finally we come to the last in the line of games spawned from our old friend the Game of Y.  *Star takes yet another leap up in complexity, and to be completely honest, I don’t fully understand how this game works.  This is partly because the instructions are written in what feels like an alien language — scoring refers to things called ‘peries’ and ‘quarks’ and it’s all a bit strange.  However the abstract strategy game community praises this game nearly universally, so I remain keen to try and figure it out.

My understanding, questionable though it may be, is that the game essentially takes the core concept of Star — connect groups of edge-adjacent pieces together to maximise your points — to the next level by adding a scoring bonus for controlling corner spaces, and a significant scoring penalty (equal to twice the difference in the number of groups between the two players) for the player with the larger number of groups.  This heavily incentivises the players to connect their groups, and the end result of this is some beautiful patterns of stones snaking across the board, as in these two sample games from the manual (one tiny one and one normal-sized one):

Here’s a closeup of that awesome board:

starstar-board1

The *Star board.  The centre star can be used by either player as a connection between groups — neither player may place their stones on it.

Note that the board has thicker lines to define smaller board sub-regions, which allows players to ease themselves into the full game.  The game is popular enough to be produced in physical form by Kadon Enterprises, who make a wooden board set for *Star that I absolutely must buy at some point:

star-wood-board2starwood

How cool is that!  Someday I shall own this game, and I shall figure out exactly how to play it.

Luckily there’s a simpler game also playable on this board — Star-Ywhere the players compete to be the first to complete a connection between two adjacent sides and one side not adjacent to either of those two.  For *Star veterans there’s also Double-Star, where players place two stones per turn and the other rules remain the same; this seems like a small change but it significantly alters the play.  New tactics and strategies are necessary to cope with the new threats that are possible with two stone placements.

So there we have it — a hectic journey from the elemental Game of Y through to the complex but highly-regarded *Star, courtesy of the brilliant minds of Craige Schensted/Ea Ea and Charles Titus.  Craige/Ea Ea has stated that *Star is ‘what the other games were trying to be’, so from his perspective each game was improving on the last, and *Star is the best of the lot.

While researching and playing/trying to play these games, I’ve found that Star and *Star are frequently compared to Go, despite having connective goals rather than territorial ones.  Given the much more flexible nature of the connective goals in these two games, I can see why — instead of connecting specific sides, players define for themselves the key parts of the board as they play.  This is much more ‘Go-like’ in that the board is more of a blank slate, and does not inherently define the direction of play as much as in other connection games.  So, if you’re a Go fan and skeptical of connection games, maybe try these two.

If you’re new to connection games in general, I’d start with Hex, then Y, then Poly-Y.  You might enjoy Star and *Star more after trying some other games with more freeform connective goals, but with easier-to-grasp rules.  I’d recommend maybe trying Havannah and Starweb for that purpose — and lucky you, they’ll be in my next post 🙂

 

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Connection Games I: Hex

As you all have probably figured out by now, I really enjoy complicated board games — dense modern board games with tons of special components, 500-year-old Shogi variants with hundreds of pieces, all that stuff.  But I also have a great fondness for games on the other end of the scale: elegant abstract games with minimal rules and maximal depth.

Now an oft-cited example of this category might be Go — it’s certainly an elegant game, with rules that are easy to summarise yet a level of depth nearly unrivalled in board games.  But Go is also hard to understand, in that the goal is clear — secure more territory than your opponent — but working out how to get there is hard.  Most beginning players, myself included, are completely flummoxed by the empty board at the start of the game, and have no idea where to start.  And at the end of the game, it’s very difficult for newbies to figure out when the game is actually over!  There’s a reason a common proverb for beginning Go players is ‘lose a hundred games as fast as possible’ — building familiarity with the basics takes time and repetition.  It’s worth it, though.

But what I’m going to talk about here are games that are so simple as to be almost elemental, as in, it’s hard to imagine games with rules simpler than these.  For my money the best examples of these types of games are in the category of connection games.  In a connection game, players vie to be the first to connect key points on the board with their pieces — a simple goal, easy to see and easy to understand.  But underneath that these games offer surprising depths of strategy and tactics.

Now, the current bible for connection games is the book by Cameron Browne called — wait for it — Connection Games, which summarises the genre beautifully and includes rules and examples of play for numerous games.  It’s a great book that I certainly can’t compete with, so in this brief series of posts I’m just going to give you some details of my picks for the best games of this type, along with some useful resources and links to where you can play.

Hex

Any discussion of connection games has to start with Hex, the originator of the whole genre.  Strangely, despite the simplicity of these games, they weren’t around until quite recently.  Hex has a tangled history — now unravelled in the recent, and excellent, book Hex, Inside and Out: The Full Storyso I won’t attempt to summarise it all here.  The game was invented by Danish mathematician Piet Hein in 1942, and was initially called Polygon.  Hein sought to create a game that reflected his interests in topological properties of the plane and the four-colour theorem, and was stuck on this idea for some time, as any attempts to build his imagined game on a square grid didn’t work, as the players could easily become deadlocked.  Eventually he realised that a hexagonal grid would prevent this issue, and thus Polygon was born:

polygon-board-1

The Polygon board, an 11×11 rhombus composed of hexagons.

The rules of Polygon are incredibly simple:

  • Players turns placing a single symbol of their chosen type — star or circle — in any empty hexagon on the board.  Once placed, symbols don’t move and can never be removed.
  • The first player to connect the sides of the board marked with their symbol with an unbroken line of their symbols is the winner.

Easy, right?  But once he started playing, Hein realised the game was far more complicated than the rules suggested.  Soon after he launched the game in the Danish magazine Politiken with the board, rules and a call for challenging Polygon puzzles from readers.  It wasn’t long before pen-and-paper Polygon pads were selling like hotcakes all over Denmark, and the game became a bonafide hit.

polygon-puzzle-1

The famous first-ever Polygon puzzle.  The circle player has the move.  How can they win?

Eventually Hein sold a 12×12 version of Polygon with a very nice wooden board called Con-Tac-Tix, which enjoyed some small success as well — and in fact you can still buy a version of this today from Hein’s grandson.  But the game didn’t really take off around the world until later, when famous mathematician John Nash (of A Beautiful Mind fame) rediscovered the game in 1948.

When Nash started sharing his discovery with colleagues at Princeton, the game rapidly gained adherents.  They often called it Nash, for obvious reasons, but legend has it some called it John instead — not because of Nash’s name, but as a nod to the fact they played it on the hexagonal tiles of the bathroom in the department!  Nash became Hex when Parker Brothers tried to market the 11×11 game with that name.  Around the same time Nash was attempting to market the game and was quite upset to discover he’d been scooped.  He wasn’t aware at that time that Piet Hein had in fact scooped him several years earlier anyway.

In any case, the game became an object of enthusiastic study by Nash and his colleagues, and they made numerous interesting discoveries about its properties.  Hex was largely just an object of interest for academics for the most part, as Parker Brothers’ attempt to sell the game didn’t amount to much.  A few years later the mathematician Martin Gardner played a pivotal role in the eventual worldwide popularisation of the game — his 1957 Scientific American column on Hex brought the game to a whole new audience.

Hex remains highly popular with mathematicians and computer scientists today, as well as with gamers, as it has some fascinating properties.  For example, draws are completely impossible in Hex — no matter how inept or random the players’ moves, eventually one of the players will always make a winning connection across the board.  This result is actually a consequence of something called the Brouwer fixed-point theorem, which I won’t get into here.  We also know that a winning strategy for the first player exists, but we have no idea what it is (well, we’ve found it by brute-force computer calculation for 9×9 boards and smaller, but not on the boards we actually play on).  A quick browse of the literature on Hex will reveal some fascinating contributions from big names in maths and computer science.

The current state of play

In the years since Piet Hein’s invention of Polygon, Hex has evolved somewhat.  The classic 11×11 board is still popular, since it has a nice balance of speed of play and intricacy.  Games on the 11×11 board are over relatively quickly, yet these 121 hexagons allow for a staggering 1056 possible board positions, 10 billion times more than the number of possible Chess positions (1046)!

However many Hex players nowadays are using larger boards, with 13×13 and 19×19 being particularly popular. 14×14 is fairly common as well, particularly as that was John Nash’s preferred board size. In any case, larger boards push the game further into the realm of strategy rather than tactics, allowing for deeper moves with greater subtlety. Here’s how a 13×13 Hex board looks today:

hex13-sample

A 13×13 Hex board.

And here is a 19×19 Hex board that I designed and just had printed on a 19×19 neoprene mat.  The mat is 93cm x 56cm, and the hexes are large enough for use with Go stones.

Hex19-1

My 19×19 Hex board.

In general we’ve abandoned the circles and stars of Polygon’s heyday and opted for the two players using black and white stones to mark their hexes, with the board edges marked accordingly.  Often you’ll see blue and red stones used instead.

More importantly, now that we know that Hex gives the first player a winning advantage, we play Hex using the swap rule, an ingenious way to even things out.  When the first player places their stone, the second player may choose to play one of their colour in response, after which the game proceeds normally, or they may choose to swap colours and take that move for their own first move!

This clever rule change means that the first player must intentionally play a weaker opening move to avoid a swap, thereby mitigating their first-player advantage instantly.  In practice the strongest opening moves are in the centre of the board, as these allow for connecting stones to extend in every direction, so generally the first player will play around the edges at the start to avoid a swap.  As you might expect, the first-player advantage is somewhat diminished on larger boards, given that the impact of individual moves is smaller in general.

Side note — the swap rule is often called the pie rule as well, as it mirrors the fairest way to divide up a slice of pie between two people: one person cuts, the other chooses which slice they will eat.

 

Playing Hex

So, once we’ve grabbed a funky rhomboid board of our preferred size, a couple piles of stones and sat round a table to play, how does the game actually work?  Here’s a quick sample game, showing me defeating a basic computer opponent on the 11×11 board:

hex11-win1

I played this game using a fantastic bit of free Java-based software called Ai Ai, which has numerous awesome abstract strategy games available to play with a variety of AI opponents — find it here: http://mrraow.com/index.php/aiai-home/aiai/

 

The play in this game was reasonably simple, but if you jump onto the most popular site for playing Hex, Little Golem, and check out the larger boards you’ll soon see that the end result of a Hex game can look pretty complicated:

hex13-sample2

A game played earlier today on Little Golem (https://www.littlegolem.net/jsp/game/game.jsp?gid=2145661)

 

Black resigned after 70 moves, admitting defeat.  The reason why Black resigned may not be immediately obvious; after all, Black seems to have made good progress along the left side!  However, we can start to understand how games of Hex evolve once we understand some basic positions, particularly the bridge:

hex-bridge

An example of a bridge: White’s stones 2 and 4 can be connected no matter what Black does.

The bridge means that connection between the two relevant stones is unstoppable.  As you can see above, if Black plays at A to attempt to break apart White’s stones, White simply plays at B, and vice versa.  The bridge is a simple example of a template, a formation of stones and empty hexes that facilitates an unstoppable connection.

If you look again at the sample games above, you’ll see several examples of bridges being used to establish connections between stones.  Using this formation is far more efficient than placing stones methodically next to one another, but the connection they provide is just as solid!  Using bridges and similar templates allows you to build connections in fewer moves.  As you learn more of these templates in Hex, you’ll be able to spot a win or a loss coming long before the final stone is placed.

By the way, now that you know what a bridge is, you should be able to solve Piet Hein’s puzzle above!

Another key concept of Hex is that defence and offence are the same thing.  Remember that in Hex one player will always win — from this we can work out that if we prevent any possible win by the opponent, that means we have to win instead!  So when playing Hex, don’t be focussed just on your own bridge-building and forget your opponent — spending your moves on blocking them still gets you closer to a win.  Sometimes the best offence is a good defence.

To get started with Hex, I suggest you just jump right in and start playing some games.  You can play Hex  on Little Golem, Richard’s PBEM Server, Amecy Games, Gorrion, Hexy.games and igGameCenter among others.  You’ll soon find that Hex is an intricate and precise game with enormous amounts of depth.  If you work on building bridges, blocking your opponent, and getting a general feel for the flow of the game, you’ll soon start to get the hang of the basics.

After losing a few times and hopefully stumbling across a win or two, go and visit Matthew Seymour’s incredibly detailed guide on Hex strategy.  His site is details key concepts like ladders and edge templates, walks you through some sample games, and provides lots of useful resources, plus everything is demonstrated through interactive diagrams!  It’s an incredible guide.  The bridge example above is a screenshot from this site, which I hope will encourage you to visit.  On the real site you can experiment and play moves on all the diagrams, which really helps cement the concepts explained in the guide.

 

Hex Variants

As you might expect with a game this elemental, numerous Hex variants have been devised over the years to spice things up.  There’s a tonne of these so I’ll just briefly highlight a few interesting ones:

Misère HexThink of this as Opposite Hex — the first player to connect their sides of the board loses!  It’s an odd style of play to get your head around, where you need to force the opponent to connect while avoiding making progress yourself.  Interestingly, it’s been proven that the losing player has a strategy that guarantees every hex on the board will be filled before the game finishes.

Pex:  The rules here are the same as Hex, but the game is played on an unusual board — instead of hexagons, the board is tiled with irregular pentagons.  This changes the tactics significantly, given that the board spaces now have different connectivity, and makes for an interesting change of pace.   You can play Pex online at igGameCenter.

pex-iggc

An 8×8 Pex board.

Nex:  This intriguing variant uses the standard Hex board, but alongside your White and Black stones you add neutral Grey stones.  Grey stones can’t be part of either player’s winning connection, so they are obstacles to both players.  But what makes this game brilliant is the new options available — a player’s turn now gives them two possible moves:

  1. The player to move may add one stone of their colour AND one neutral stone to any empty hexes on the board, OR
  2. They may swap out two neutral stones for stones of their colour, and then replace one stone of their colour with a neutral one.

This means that moves are not permanent in Nex — your stones can be recycled when the board situation changes, and seemingly innocuous neutral stones can suddenly become new threats for either side when they transform.

Just like in Hex, there are no ties and one player must win.  You can play Nex on igGameCenter.

nex-sample-game1

A sample Nex game from the book Mathematical Games, Abstract Games — Black resigned.

Chameleon: Another intriguing variant that significantly changes up the play, Chameleon decouples players from colours.  In Chameleon, one player is Vertical and must make a connection of either colour from top to bottom, and the other is Horizontal and must make a connection of either colour from side to side.  On each turn a player may place a Black stone OR a White stone on the board on any empty hex.

The consequence of this is that players have to be aware of threats in the opponent’s direction from stones of either colour, making each move feel incredibly consequential!  It’s a bit of a mind-bender.  Chameleon benefits from playing on larger boards, as connections can happen too quickly on smaller ones given that players use both colours.  You can play it online using Richard’s PBEM Server.

 

What next?

Now that you’ve had an intro to the original connection game, you’ll be well-equipped to try your hand at Hex’s many fascinating cousins.  The basic concepts of Hex are helpful in a lot of other connection games too, although each of them adds their own unique wrinkles.

Over the next few posts, I’ll highlight some more connection games with interesting properties that are fun to play, including the Game of Y, TwixT, Havannah, ConHex, Unlur, and more.

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